Re: Octave Software - Null function
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.
.
Relevant Pages
- 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... ...
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