Definite matrix: Difference between revisions

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Revision as of 00:43, 21 February 2003

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The '''positive definite''' [[matrix (mathematics)|matrices]] are in several senses analogous to the positive [[real number]]s. An ''n'' × ''n'' [[Hermitian]] [[matrix (mathematics)|matrix]] ''M'' is said to be '''positive definite''' if it has one (and therefore all) of the following 6 equivalent properties:

'''(1)''' For all non-zero vectors ''z'' in '''C'''^''n'' we have