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Sylvester's criterion
Criterion for positivity of a Hermitian matrix
Sylvester's criterion
In mathematics, Sylvester's criterion is a necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite, due to James Joseph Sylvester. Let M {\displaystyle M} be an n × n Hermitian matrix, meaning M = M † {\displaystyle M=M^{\dagger }} , where † {\displaystyle \dagger } denotes the complex conguate transpose operation. Sylvester's criterion states that M {\displaystyle M} is positive-definite, meaning x → † M x → >...
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