New proofs for a bound on the spectral radius of the Hadamard geometric mean
Jacob Adamczyk – GJM, Volume 9, Issue 2 (2024), 10-14.
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- décembre 25, 2024
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In this short note, we present two new proofs of an inequality first derived by Elsner, Johnson, and Dias Da Silva for an upper bound on the Perron root of the geometric mean of non-negative irreducible matrices. The first proof technique uses the Collatz-Wielandt characterization of the spectral radius; the second establishes a new bound at the matrix element level and a sub-multiplicative property of matrix norms, both of which easily follow from Hölder’s inequality.
Categories: Issue2
Milestones:
Received: May 25, 2024
Accepted: November 07, 2024
Revised: September 08, 2024
Authors:
Jacob AdamczykDepartment of Physics, 100 Morrissey Blvd.,
Boston, 02125, MA, USA