Definite matrix: Difference between revisions

Revision as of 15:52, 22 February 2002

Revision as of 22:29, 23 February 2002

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for all non-zero ''x'' in '''R'''^''n'' (or, equivalently, all non-zero ''x'' in '''C'''^''n''). It is called '''positive semidefinite''' if

:<i>x</i>^*<i> M x</i> >=&ge; 0

for all ''x'' in '''R'''^''n'' (or '''C'''^''n'') and '''negative semidefinite''' if

:<i>x</i>^*<i> M x</i> &le; 0

x</i> <= 0 for all ''x'' in '''R'''^''n'' (or '''C'''^''n'').

A Hermitian matrix which is neither positive nor negative semidefinite is called '''indefinite'''.