If I'm not mistaken, the Cholesky decomposition only exists if the matrix is
both Hermitian and positive definite.
To guarantee that, you need to assume both determinant(D)>0 *and also* a>0.
Then Maxima finds the decomposition:
(%i2) D:matrix([a,b],[b,c])$
(%i3) cholesky(D);
Unable to find the Cholesky factorization
-- an error. To debug this try: debugmode(true);
(%i4) assume(determinant(D)>0)$
(%i5) cholesky(D);
Unable to find the Cholesky factorization
-- an error. To debug this try: debugmode(true);
(%i6) assume(a>0)$
(%i7) cholesky(D);
(%o7) matrix([sqrt(a),0],[b/sqrt(a),sqrt(c-b^2/a)])
<<<<<<<<<<<<<<<<<<<<<<<<
Tested in Maxima 5.23.2 GCL 2.6.8 WIndows 7
-s
On Mon, Aug 15, 2011 at 10:18, gabriele <dante_monti2 at yahoo.it> wrote:
> ith wxmaxima 0.7.1 ubuntu hardy
> D:matrix([a,b],[b,c]);
> cholesky(D);
> Unable to find the Cholesky factorization -- an error. To debug this try
> debugmode(true);
>
> even with
>
> assume(determinant(D)>0);
> cholesky(D);
> Unable to find Cholesky etc...
>
> but
>
> cholesky(transpose(D).D);
> Is b2+a2 positive or zero?positive;
> result...
> which means cholesky symbolic works..
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