Eigenvalues of a principal submatrix?

19 March 2023 1 5K Report

I have a nonnegative square matrix A and a matrix B that is a principal submatrix of A. Is there anything I can say about how the eigenvalues of B are related to the eigenvalues of A? I'm not assuming that A is symmetric here.

-Rich

Yuri S Semenov

I can propose a hypotesis for positive matrices: the maximal eigenvalue of B is less or equal to the maximal eigenvalue of A (both are real due to Frobenius-Perron theorem). Maybe, the Collatz-Wieland formula will be helpful for proving this (if it is true).

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