[Numpy-discussion] Should cholesky return upper or lower triangular matrix?

Keith Goodman kwgoodman at gmail.com
Tue Jun 27 22:25:08 CDT 2006


On 6/27/06, Robert Kern <robert.kern at gmail.com> wrote:
> Keith Goodman wrote:
> > Isn't the Cholesky decomposition by convention an upper triangular
> > matrix? I noticed, by porting Octave code, that linalg.cholesky
> > returns the lower triangular matrix.
> >
> > References:
> >
> > http://mathworld.wolfram.com/CholeskyDecomposition.html
> > http://www.mathworks.com/access/helpdesk/help/techdoc/ref/chol.html
>
> Lower:
> http://en.wikipedia.org/wiki/Cholesky_decomposition
> http://www.math-linux.com/spip.php?article43
> http://planetmath.org/?op=getobj&from=objects&id=1287
> http://rkb.home.cern.ch/rkb/AN16pp/node33.html#SECTION000330000000000000000
> http://www.riskglossary.com/link/cholesky_factorization.htm
> http://www.library.cornell.edu/nr/bookcpdf/c2-9.pdf
>
> If anything, the convention appears to be lower-triangular.

If you give me a second, I'll show you that the wikipedia supports my claim.

OK. Lower it is. It will save me a transpose when I calculate joint
random variables.




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