the SVD (singular value decomposition) stuff

ok, i’ve published everything i planned to put out there for the SVD. not to say i won’t need to add things, if anyone ever has any questions about what i meant….

yes, i need to put out a bibliography, too. but i’ve been at this all day, and it’s time to stop. incidentally, the SVD stuff is a category of its own – not a page as i originally set up the first (last!) installment.

i should probably emphasize that the SVD category is posted in the order i intend it to be read.

it looks like quite a pile of stuff, and it’s scary to think that it’s all only background for principal components analysis!

one advantage to doing as much work as i did today is that i’ve managed to streamline the process. take a piece of the latex output from mathematica®, drop it into TextWrangler, edit it massively there, then copy a preliminary version into the wordpress editor, and finally edit there until it works.

well, i’m thrilled to have found a way to play with the SVD, after all the years i’ve meant to. i need to actually write down the list of all the other things i’ve been meaning to look at.

3 Responses to “the SVD (singular value decomposition) stuff”

1. rip Says:

1) In some places it looked like you were interchanging inverse and transpose. They
are obviously different operations, under what circumstances do they yield the same
result? What part of “Linear Algebra” should I reread?

a real square matrix is called orthogonal if (i have to try this) $A^T A = I$ . that implies that

the columns of A are a set of orthonormal vectors
the matrix is invertible
A^-1 = A^T
A A^T = I
the matrix is a rotation

to answer your specific question, the transpose = the inverse iff the matrix is orthogonal.

NOTE my remarks about an orthonormal matrix being one that doesn’t have enough columns.

the corresponding property for a complex matrix is “unitary”, and requires that the conjugate transpose = the inverse.

look up “orthogonal matrix” and “unitary matrix”.

2. rip Says: