Definite matrix: Difference between revisions

Revision as of 21:47, 19 November 2003

Revision as of 18:16, 29 February 2004

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'''(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 - I think...)

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