Sylvester's Criterion
In mathematics, Sylvester’s criterion is a necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite. It is named after James Joseph Sylvester.
Sylvester's criterion states that a 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 ,
- the upper left 2-by-2 corner of ,
- the upper left 3-by-3 corner of ,
- ...
- itself.
In other words, all of the leading principal minors must be positive.
Read more about Sylvester's Criterion: Proof
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