Re: [Algorithms] decompose onto non-orthogonal vectors

[<ro...@do...>]

I  wrote:

>Jonathan Blow  wrote:
>
>>Just build a transformation matrix from R to S, and
>>call that matrix T.  Then p' = Tp and you are done.
>>
>>For instructions on how to make a matrix that goes from
>>one space to another, given the basis vectors of each 
>>space, consult any one of a trillion graphics books.
>
>Again, you don't need matrices (maybe chapter 3) but just high school
>algebra.
>

Since I was rushing out the door to a Bastille Day party I didn't get
a chance to add that your "change of basis" approach DOES have the
benefit that when you get this matrix, then you can solve the same
problem for ANY OTHER vector p, simply by a matrix multiplication.  

But again, that was a much more complicated problem than that which
was asked, involving just one given vector p.  And also it would apply
only in the case that Ben was thinking of a 2D problem and we have
learned from a subsequent post that it is the 3D problem he had in
mind. (It takes three indepdent vectors, not two, to form a basis of
3-space).

P.S. The Bastille Day party was great fun.  It was held in the studio
of a Berkeley company called Scientific Arts, the folks who built the
giant baseball mitt and Coke-bottle kiddy slide that grace the
lefr-field bleachers of the new SF Giants ballpark.  For the party
they'd built a perfectly working model guillotine, about three feet
tall, and used it to chop up the frogs for the frog-leg barbecue.