Basically, a singular value decomposition of a matrix A results in three matrices U, S and V such that U and V are unitary, S is diagonal
and A = U * S * V' or A * V = U * S. So by choosing those columns of V
such that A * V = 0, you get a unitary basis for the null space of A.
This is exactly what Matlab and Octave do. This is probably a shoddy
explanation, but any good textbook on linear algebra should have a
better one.
Singular Value Decomposition ... I'm always interested in linear algebra, and I find interesting the Singular Value Decomposition and its implications. ... If M is square, then are U, V and S related to the diagonalization?... (sci.math)
Re: pseudo inverse ... >from the singular value decomposition...Dave...Prev by Date: ... (sci.math.num-analysis)
Re: help in algorithm ... this sounds like LSI / singular value decomposition...Prev by Date: ... (comp.lang.python)
[ANN] Ruby Linear Algebra Library 1.0.0 ... = Linalg - Ruby Linear Algebra Library... A Fortran-based linear algebra package....Cholesky decomposition... This release consists of installer changes for Mac and libg2c support. ... (comp.lang.ruby)
Re: Eigenvalues and transformations ... Is there any connection between the eigenvalues/eigenvectors of X and A? ... I read about the singular value decomposition, and since P is real and A is real too, it can be decomposed into three matrices, the same can be done on Q and I can say this, if I'm not mistaken: ... V is such that V^T V = V V^T = I, the same is for U (if I understand, since they are real matrices).... In the last line, the matrix S ``preserves'' positive definiteness since singular values are non-negative, but U is just unitary... ... (sci.math)
