I know that a Hermitian matrix is positive definite if and only if all of it's leading principal minors are positive. But now I had a discussion in which someone claimed that positive definiteness of a Hermitian matrix implies that all principal minors (i.e. not just the leading ones) are positive. Is this true? How can I prove it? I could not find a definite reference for this.
2026-03-26 02:56:02.1774493762
Positive definite Hermitian matrices and non-leading principal minors
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