CSE 401/CS 450/MATH 450/ECE 491: Message 231

Date: Wed, 25 Oct 2006 08:24:55
From: S Bond
Subject: Re: definiteness

Jonathan W. Ray wrote:
> What is the easiest way to determine whether a matrix is positive definite?

If the matrix is symmetric, try to compute the Cholesky factorization,
it will only fail if the matrix is not positive definite.

> What is the easiest way to determine whether a matrix is negative definite? 

Same as for positive definite, but with the negative of the matrix, i.e.
let A = -B.

Computing the Cholesky factorization, typically, requires
fewer operations than computing all the eigenvalues.  You can
also find the "matrix inertia" which counts the number of
positive, negative, and zero eigenvalues.  Algorithms for
computing this usually use the L D L^T factorization.  See
page 195 in the book, for example.  This is basically
the same amount of work as Choleksy.

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