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Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices

✍ Scribed by Don Coppersmith; Alan J. Hoffman; Uriel G. Rothblum

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 844 KB
Volume: 263
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00534-4

No coin nor oath required. For personal study only.

✦ Synopsis

Given a square, nonnegative, symmetric matrix A, the Rayleigh quotient of a nonnegative vector u under A is given by QA(u)= urAu//uru. We show that QA(~/u o Au ) is not less than QA(u), where ~--denotes coordinatewise square roots and o is the Hadamard product, but that QA(Au) may be smaller than QA(U).

Further, we examine issues of convergence.

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