Definite matrix: Difference between revisions

Revision as of 01:17, 13 March 2005

Revision as of 14:19, 26 April 2005

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In [[linear algebra]], the positive-definite [[matrix (mathematics)|matrices]] are (in several ways) analogous to the positive [[real number]]s. An ''n'' &times; ''n'' [[Hermitian matrix]] <math>M</math> is said to be '''positive definite''' if it has one (and therefore all) of the following six equivalent properties.

First, define some things:

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*<math>\mathbb{Z}</math> is the set of all [[integer]]s

*<math>M</math> is any Hermitian matrix

An ''n'' &times; ''n'' [[Hermitian matrix]] <math>M</math> is said to be '''positive definite''' if it has one (and therefore all) of the following six equivalent properties:

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