Definite matrix: Difference between revisions

Revision as of 15:30, 22 February 2002

Revision as of 15:50, 22 February 2002

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An ''n'' × ''n'' [[Hermitian]] [[matrix]] ''M'' is said to be '''positive definite''' (we mark M > 0) if

:<i>x</i>' <i>M x</i> > 0

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for all ''x'' in '''R'''^''n''.

It is said to be '''negative definite''' (we mark M < 0) if

:<i>x</i>' <i>M x</i> < 0

'''positive semidefinite''' (we mark M >= 0) if

:<i>x</i>'<i> M x</i> >= 0

and '''negative semidefinite''' (we mark M <= 0) if

:<i>x</i>'<i> M x</i> <= 0

Otherwise we say matrix is '''indefinite''' (we mark M <> 0).