Definite matrix: Difference between revisions

Revision as of 21:13, 22 October 2005

Revision as of 05:57, 9 December 2005

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defines an [[inner product]] on <math>\mathbb{C}^n</math>. (In fact, every inner product on <math>\mathbb{C}^n</math> arises in this fashion from a Hermitian positive definite matrix.)

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|valign="top"| '''4.''' || All the following matrices (the leading principleprincipal minors) have a positive [[determinant]] (the Sylvester criterion):

* the upper left 1-by-1 corner of <math>M</math>

* the upper left 2-by-2 corner of <math>M</math>