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An estimation of the spectral radius of a product of block matrices

✍ Scribed by Mei-Qin Chen; Xiezhang Li

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
186 KB
Volume
379
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let C(r) = [C ij ], r = 1, 2, . . . , R, be block m Γ— m matrices where C ij (r) are nonnegative N i Γ— N j matrices for i, j = 1, 2, . . . , m. Let β€’ be a consistent matrix norm. Denote for each r by B(r) = [ C ij (r) ] an m Γ— m matrix. The relation of the spectral radii ρ( R r=1 C(r)) and ρ( R r=1 B(r)) is studied in this paper. It is shown with two proofs that ρ  ο£­ R r=1 C(r) ο£Ά ο£Έ ρ  ο£­ R r=1 B(r) ο£Ά ο£Έ .

As shown in one of the proofs, ρ( R r=1 B(r)) can be reduced so that it gives a better estimation of ρ( R r=1 C(r)).

πŸ“œ SIMILAR VOLUMES

On the spectral radius and the spectral
On the spectral radius and the spectral norm of Hadamard products of nonnegative matrices
✍ Zejun Huang πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 140 KB

## We prove the spectral radius inequality ρ(A for nonnegative matrices using the ideas of Horn and Zhang. We obtain the inequality A β€’ B ρ(A T B) for nonnegative matrices, which improves Schur's classical inequality , where β€’ denotes the spectral norm. We also give counterexamples to two conject