Definite matrix: Difference between revisions

Revision as of 13:51, 2 October 2004

Revision as of 17:48, 2 December 2004

Line 3:

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

:<i>z</i>^* <i>M z</i> > 0.

Here we view ''z'' as a [[column vector]] with ''n'' [[complex number|complex]] entries and ''z''^* as the [[conjugate transpose|complex conjugate of its transpose]]. (''M'' being Hermitian, ''z''^* ''M'' ''z'' is always real.)

'''(2)''' For all non-zero vectors ''x'' in