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arXiv · 1301.4665

Nonnegative definite hermitian matrices with increasing principal minors

Shmuel Friedland
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Abstract

A nonzero nonnegative definite hermitian m by m matrix A has increasing principal minors if the value of each principle minor of A is not less than the value each of its subminors. For $m>1$ we show $A$ has increasing principal minors if and only if $A^{-1}$ exists and its diagonal entries are less or equal to 1.

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Shmuel Friedland. 2013-01-20. Nonnegative definite hermitian matrices with increasing principal minors. https://arxiv.org/abs/1301.4665

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