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From: SourceForge.net <noreply@so...>  20041111 01:05:12

Bugs item #1064238, was opened at 20041110 17:05 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041111 23:04:21

Bugs item #1064238, was opened at 20041110 20:05 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  >Comment By: Raymond Toy (rtoy) Date: 20041111 18:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041119 20:19:00

Bugs item #1064238, was opened at 20041110 17:05 Message generated for change (Comment added) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 12:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 15:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041119 21:56:47

Bugs item #1064238, was opened at 20041110 20:05 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  >Comment By: Raymond Toy (rtoy) Date: 20041119 16:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 15:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 18:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041119 23:24:39

Bugs item #1064238, was opened at 20041110 17:05 Message generated for change (Comment added) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 15:24 Message: Logged In: NO I don't trust you. You can't obtain the desired matrix via elementary row operations ( or we don't have the same definition of elementary row operations ). if you don't know that the determinant must match, look at http://www.mathematicsonline.org/kurse/kurs10/seite151.html and http://en.wikipedia.org/wiki/Determinant or http://en.wikipedia.org/wiki/Similar. You will learn that a matrix and a triangular form of this matrix are similar ( first link) and that two similar matrix have the same determinant (second and third links). I've found the links with a simple google search . Next time, please search before you ask  Comment By: Raymond Toy (rtoy) Date: 20041119 13:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 12:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 15:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041120 14:21:50

Bugs item #1064238, was opened at 20041110 20:05 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  >Comment By: Raymond Toy (rtoy) Date: 20041120 09:21 Message: Logged In: YES user_id=28849 For me elementary row operations include swapping rows. That doesn't preserve the determinant. Anyway, I don't want to argue over this. Convince someone else you are right and have them fix it for you.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 18:24 Message: Logged In: NO I don't trust you. You can't obtain the desired matrix via elementary row operations ( or we don't have the same definition of elementary row operations ). if you don't know that the determinant must match, look at http://www.mathematicsonline.org/kurse/kurs10/seite151.html and http://en.wikipedia.org/wiki/Determinant or http://en.wikipedia.org/wiki/Similar. You will learn that a matrix and a triangular form of this matrix are similar ( first link) and that two similar matrix have the same determinant (second and third links). I've found the links with a simple google search . Next time, please search before you ask  Comment By: Raymond Toy (rtoy) Date: 20041119 16:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 15:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 18:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041120 22:33:51

Bugs item #1064238, was opened at 20041110 17:05 Message generated for change (Comment added) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  Comment By: Nobody/Anonymous (nobody) Date: 20041120 14:33 Message: Logged In: NO I'm not sure to understand the output %3 but is it saying that the second row is nul ? If so this say that det(trianularize(a))=0 but this impossible because det(a)!=0. Indeed swap rows do *not* conserve det(a) but *do* conserve det(a) . So in fact by your argument rtoy your saying that this report *is* a bug. Please consider this (even if the submiter was not really nice) ! Thanks in advance, a ph.d student in maths.  Comment By: Raymond Toy (rtoy) Date: 20041120 06:21 Message: Logged In: YES user_id=28849 For me elementary row operations include swapping rows. That doesn't preserve the determinant. Anyway, I don't want to argue over this. Convince someone else you are right and have them fix it for you.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 15:24 Message: Logged In: NO I don't trust you. You can't obtain the desired matrix via elementary row operations ( or we don't have the same definition of elementary row operations ). if you don't know that the determinant must match, look at http://www.mathematicsonline.org/kurse/kurs10/seite151.html and http://en.wikipedia.org/wiki/Determinant or http://en.wikipedia.org/wiki/Similar. You will learn that a matrix and a triangular form of this matrix are similar ( first link) and that two similar matrix have the same determinant (second and third links). I've found the links with a simple google search . Next time, please search before you ask  Comment By: Raymond Toy (rtoy) Date: 20041119 13:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 12:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 15:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041121 14:29:49

Bugs item #1064238, was opened at 20041110 20:05 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  >Comment By: Raymond Toy (rtoy) Date: 20041121 09:29 Message: Logged In: YES user_id=28849 The bug report doesn't display the actual results very well. The result is matrix([4, 0, 2],[0,4,0],[0,0,2]); For me, elementary row operations include multiplying a row by a constant. That definitely gives a different determinant. Anyway, I can obtain the given result by multiplying row 1 by 5 and row 3 by 4 and adding them to give a new matrix, matrix([4,0,2],[0,1,0],[0,4,2]). Then multiply row 2 by 4 and add it to row 3 to get matrix([4,0,2],[0,1,0],[0,0,2]). Each of these I consider elementary row operations, and clearly the determinant is not the same as the original. It seems to me you really want a very specific way of triangularizing a matrix.  Comment By: Nobody/Anonymous (nobody) Date: 20041120 17:33 Message: Logged In: NO I'm not sure to understand the output %3 but is it saying that the second row is nul ? If so this say that det(trianularize(a))=0 but this impossible because det(a)!=0. Indeed swap rows do *not* conserve det(a) but *do* conserve det(a) . So in fact by your argument rtoy your saying that this report *is* a bug. Please consider this (even if the submiter was not really nice) ! Thanks in advance, a ph.d student in maths.  Comment By: Raymond Toy (rtoy) Date: 20041120 09:21 Message: Logged In: YES user_id=28849 For me elementary row operations include swapping rows. That doesn't preserve the determinant. Anyway, I don't want to argue over this. Convince someone else you are right and have them fix it for you.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 18:24 Message: Logged In: NO I don't trust you. You can't obtain the desired matrix via elementary row operations ( or we don't have the same definition of elementary row operations ). if you don't know that the determinant must match, look at http://www.mathematicsonline.org/kurse/kurs10/seite151.html and http://en.wikipedia.org/wiki/Determinant or http://en.wikipedia.org/wiki/Similar. You will learn that a matrix and a triangular form of this matrix are similar ( first link) and that two similar matrix have the same determinant (second and third links). I've found the links with a simple google search . Next time, please search before you ask  Comment By: Raymond Toy (rtoy) Date: 20041119 16:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 15:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 18:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041121 16:20:29

Bugs item #1064238, was opened at 20041110 17:05 Message generated for change (Comment added) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  Comment By: Nobody/Anonymous (nobody) Date: 20041121 08:20 Message: Logged In: NO it really seems to me that there is a bug. Take a matrix A, non singular. The matrix R is triangularize(A) if, and only if, a matrix Q exist wich match: R = Q^1 * A * Q Ok with that ? So, here is the proof that det(A) == det(R): det(R) = det(Q^1 * A * Q) det(R) = det(Q^1) * det(A) * det(Q) det(R) = det(Q)^1 * det(A) * det(Q) det(R) = det(Q)/det(Q) * det(A) det(R) = 1 * det(A) So, det(R) = det(A) Are you Ok with this demonstration ?  Comment By: Raymond Toy (rtoy) Date: 20041121 06:29 Message: Logged In: YES user_id=28849 The bug report doesn't display the actual results very well. The result is matrix([4, 0, 2],[0,4,0],[0,0,2]); For me, elementary row operations include multiplying a row by a constant. That definitely gives a different determinant. Anyway, I can obtain the given result by multiplying row 1 by 5 and row 3 by 4 and adding them to give a new matrix, matrix([4,0,2],[0,1,0],[0,4,2]). Then multiply row 2 by 4 and add it to row 3 to get matrix([4,0,2],[0,1,0],[0,0,2]). Each of these I consider elementary row operations, and clearly the determinant is not the same as the original. It seems to me you really want a very specific way of triangularizing a matrix.  Comment By: Nobody/Anonymous (nobody) Date: 20041120 14:33 Message: Logged In: NO I'm not sure to understand the output %3 but is it saying that the second row is nul ? If so this say that det(trianularize(a))=0 but this impossible because det(a)!=0. Indeed swap rows do *not* conserve det(a) but *do* conserve det(a) . So in fact by your argument rtoy your saying that this report *is* a bug. Please consider this (even if the submiter was not really nice) ! Thanks in advance, a ph.d student in maths.  Comment By: Raymond Toy (rtoy) Date: 20041120 06:21 Message: Logged In: YES user_id=28849 For me elementary row operations include swapping rows. That doesn't preserve the determinant. Anyway, I don't want to argue over this. Convince someone else you are right and have them fix it for you.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 15:24 Message: Logged In: NO I don't trust you. You can't obtain the desired matrix via elementary row operations ( or we don't have the same definition of elementary row operations ). if you don't know that the determinant must match, look at http://www.mathematicsonline.org/kurse/kurs10/seite151.html and http://en.wikipedia.org/wiki/Determinant or http://en.wikipedia.org/wiki/Similar. You will learn that a matrix and a triangular form of this matrix are similar ( first link) and that two similar matrix have the same determinant (second and third links). I've found the links with a simple google search . Next time, please search before you ask  Comment By: Raymond Toy (rtoy) Date: 20041119 13:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 12:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 15:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20041121 16:28:06

Bugs item #1064238, was opened at 20041110 17:05 Message generated for change (Comment added) made by nobody You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  Comment By: Nobody/Anonymous (nobody) Date: 20041121 08:28 Message: Logged In: NO BTW, triangularize is not a LU decomposition ! It seem that there is a such confusion with this thread. LU decomposition can be obtained by elementary row operations ( with the Gauss pivot algorith ), but I think that the triangularize function should calculate the matrix R as shown as above ( by calculating the eigenvalues/vector ). So no elementary row operation should be involved with the triangularize function.  Comment By: Nobody/Anonymous (nobody) Date: 20041121 08:20 Message: Logged In: NO it really seems to me that there is a bug. Take a matrix A, non singular. The matrix R is triangularize(A) if, and only if, a matrix Q exist wich match: R = Q^1 * A * Q Ok with that ? So, here is the proof that det(A) == det(R): det(R) = det(Q^1 * A * Q) det(R) = det(Q^1) * det(A) * det(Q) det(R) = det(Q)^1 * det(A) * det(Q) det(R) = det(Q)/det(Q) * det(A) det(R) = 1 * det(A) So, det(R) = det(A) Are you Ok with this demonstration ?  Comment By: Raymond Toy (rtoy) Date: 20041121 06:29 Message: Logged In: YES user_id=28849 The bug report doesn't display the actual results very well. The result is matrix([4, 0, 2],[0,4,0],[0,0,2]); For me, elementary row operations include multiplying a row by a constant. That definitely gives a different determinant. Anyway, I can obtain the given result by multiplying row 1 by 5 and row 3 by 4 and adding them to give a new matrix, matrix([4,0,2],[0,1,0],[0,4,2]). Then multiply row 2 by 4 and add it to row 3 to get matrix([4,0,2],[0,1,0],[0,0,2]). Each of these I consider elementary row operations, and clearly the determinant is not the same as the original. It seems to me you really want a very specific way of triangularizing a matrix.  Comment By: Nobody/Anonymous (nobody) Date: 20041120 14:33 Message: Logged In: NO I'm not sure to understand the output %3 but is it saying that the second row is nul ? If so this say that det(trianularize(a))=0 but this impossible because det(a)!=0. Indeed swap rows do *not* conserve det(a) but *do* conserve det(a) . So in fact by your argument rtoy your saying that this report *is* a bug. Please consider this (even if the submiter was not really nice) ! Thanks in advance, a ph.d student in maths.  Comment By: Raymond Toy (rtoy) Date: 20041120 06:21 Message: Logged In: YES user_id=28849 For me elementary row operations include swapping rows. That doesn't preserve the determinant. Anyway, I don't want to argue over this. Convince someone else you are right and have them fix it for you.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 15:24 Message: Logged In: NO I don't trust you. You can't obtain the desired matrix via elementary row operations ( or we don't have the same definition of elementary row operations ). if you don't know that the determinant must match, look at http://www.mathematicsonline.org/kurse/kurs10/seite151.html and http://en.wikipedia.org/wiki/Determinant or http://en.wikipedia.org/wiki/Similar. You will learn that a matrix and a triangular form of this matrix are similar ( first link) and that two similar matrix have the same determinant (second and third links). I've found the links with a simple google search . Next time, please search before you ask  Comment By: Raymond Toy (rtoy) Date: 20041119 13:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 12:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 15:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
From: SourceForge.net <noreply@so...>  20051101 15:51:01

Bugs item #1064238, was opened at 20041110 18:05 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. >Category: Documentation Group: None >Status: Closed >Resolution: Fixed Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: triangularize gives wrong results Initial Comment: for example : (%i1) a:matrix([4,0,2],[0,1,0],[5,1,3]); [  4 0  2 ] [ ] (%o1) [ 0 1 0 ] [ ] [ 5 1 3 ] (%i2) determinant(a); (%o2)  2 (%i3) t:triangularize(a); [  4 0  2 ] [ ] (%o3) [ 0  4 0 ] [ ] [ 0 0  2 ] a and t doesn't even have the same determinant.  >Comment By: Robert Dodier (robert_dodier) Date: 20051101 08:50 Message: Logged In: YES user_id=501686 triangularize appears to carry out Gaussian elimination, and is observed to yield the same thing as echelon except that the leading coefficient isn't necessarily 1. I've updated Matices.texi to say that. Also the description of triangularize now mentions LU and Cholesky as other things. Closing this report as fixed.  Comment By: Nobody/Anonymous (nobody) Date: 20041121 09:28 Message: Logged In: NO BTW, triangularize is not a LU decomposition ! It seem that there is a such confusion with this thread. LU decomposition can be obtained by elementary row operations ( with the Gauss pivot algorith ), but I think that the triangularize function should calculate the matrix R as shown as above ( by calculating the eigenvalues/vector ). So no elementary row operation should be involved with the triangularize function.  Comment By: Nobody/Anonymous (nobody) Date: 20041121 09:20 Message: Logged In: NO it really seems to me that there is a bug. Take a matrix A, non singular. The matrix R is triangularize(A) if, and only if, a matrix Q exist wich match: R = Q^1 * A * Q Ok with that ? So, here is the proof that det(A) == det(R): det(R) = det(Q^1 * A * Q) det(R) = det(Q^1) * det(A) * det(Q) det(R) = det(Q)^1 * det(A) * det(Q) det(R) = det(Q)/det(Q) * det(A) det(R) = 1 * det(A) So, det(R) = det(A) Are you Ok with this demonstration ?  Comment By: Raymond Toy (rtoy) Date: 20041121 07:29 Message: Logged In: YES user_id=28849 The bug report doesn't display the actual results very well. The result is matrix([4, 0, 2],[0,4,0],[0,0,2]); For me, elementary row operations include multiplying a row by a constant. That definitely gives a different determinant. Anyway, I can obtain the given result by multiplying row 1 by 5 and row 3 by 4 and adding them to give a new matrix, matrix([4,0,2],[0,1,0],[0,4,2]). Then multiply row 2 by 4 and add it to row 3 to get matrix([4,0,2],[0,1,0],[0,0,2]). Each of these I consider elementary row operations, and clearly the determinant is not the same as the original. It seems to me you really want a very specific way of triangularizing a matrix.  Comment By: Nobody/Anonymous (nobody) Date: 20041120 15:33 Message: Logged In: NO I'm not sure to understand the output %3 but is it saying that the second row is nul ? If so this say that det(trianularize(a))=0 but this impossible because det(a)!=0. Indeed swap rows do *not* conserve det(a) but *do* conserve det(a) . So in fact by your argument rtoy your saying that this report *is* a bug. Please consider this (even if the submiter was not really nice) ! Thanks in advance, a ph.d student in maths.  Comment By: Raymond Toy (rtoy) Date: 20041120 07:21 Message: Logged In: YES user_id=28849 For me elementary row operations include swapping rows. That doesn't preserve the determinant. Anyway, I don't want to argue over this. Convince someone else you are right and have them fix it for you.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 16:24 Message: Logged In: NO I don't trust you. You can't obtain the desired matrix via elementary row operations ( or we don't have the same definition of elementary row operations ). if you don't know that the determinant must match, look at http://www.mathematicsonline.org/kurse/kurs10/seite151.html and http://en.wikipedia.org/wiki/Determinant or http://en.wikipedia.org/wiki/Similar. You will learn that a matrix and a triangular form of this matrix are similar ( first link) and that two similar matrix have the same determinant (second and third links). I've found the links with a simple google search . Next time, please search before you ask  Comment By: Raymond Toy (rtoy) Date: 20041119 14:56 Message: Logged In: YES user_id=28849 I can obtain the desired matrix via elementary row operations. Please cite a reference that says the determinant must match.  Comment By: Nobody/Anonymous (nobody) Date: 20041119 13:18 Message: Logged In: NO to rtoy "Why is this wrong? The result is an upper triangular matrix." This is a joke ? You know [1 2 3],[0,5,6],[0,0,7] is too an upper triangular matrix. I thought the command triangularize(a) gives a triangular form of the matrix a an not an random upper triangular matrix. It seems you didn't read my comment "a and t doesn't even have the same determinant." . I hope you know that a matrix and a triangular form of this matrix should have the same determinant.  Comment By: Raymond Toy (rtoy) Date: 20041111 16:04 Message: Logged In: YES user_id=28849 Why is this wrong? The result is an upper triangular matrix.  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1064238&group_id=4933 
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