Sylvester's criterion
id:
sylvester-s-criterion-302-7415837
title:
Sylvester's criterion
text:
In mathematics, Sylvester’s criterion is a necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite. Sylvester's criterion states that a n × n Hermitian matrix M is positive-definite if and only if all the following matrices have a positive determinant: the upper left 1-by-1 corner of M,
the upper left 2-by-2 corner of M,
the upper left 3-by-3 corner of M, ⋮ M itself. In other words, all of the leading principal minors must be positive. By using appropriate
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wiki
category slug:
encyclopedia
description:
Criterion of positive definiteness of a matrix
original url:
https://en.wikipedia.org/wiki/Sylvester%27s_criterion
date created:
date modified:
2024-04-21T16:41:38Z
main entity:
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