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Re: Matrices and "type tags"

From: Mike Miller
Subject: Re: Matrices and "type tags"
Date: Thu, 9 Dec 1999 11:23:04 -0600 (CST)

On Thu, 9 Dec 1999, Thomas Hoffmann wrote:

> The state-of-the-art in Octave is, that we have complex and real
> matrix types recognized by the system and handled accordingly, but
> that we have to look for the other "special"  properties of matrices
> ourselves (e.g. one can (wrongly) give a non-symmetric matrix to
> chol()).

Thanks for pointing this out.  I never thought about what chol would do
with a square, asymmetric, positive-definite matrix.  It is the same in
both Octave and MATLAB:

octave:4> X=rand(3)+eye(3), e= eig(X)
X =

  1.49100  0.62694  0.13827
  0.13255  1.16509  0.54857     <---clearly asymmetric
  0.26631  0.76653  1.91000

e =

  2.41438                       <---clearly positive definite

octave:5> chol(X)'*chol(X) - X
ans =                           <---no error messages

  -0.00000   0.00000   0.00000
   0.49439   0.00000   0.00000  <---a reasonable solution
  -0.12805  -0.21796   0.00000

The lower triangle of the input matrix is ignored in computing the
Cholesky factorization.  So I'll be extra careful to have symmetric input!



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