Title

An Estimation of the Spectral Radius of a Product of Block Matrices

Document Type

Article

Publication Date

3-1-2004

Publication Title

Linear Algebra and Its Applications

DOI

10.1016/S0024-3795(03)00545-7

ISSN

0024-3795

Abstract

Let C(r)=[Cij], r=1,2,…,R, be block m×m matrices where Cij(r) are nonnegative Ni×Nj matrices for i,j=1,2,…,m. Let ∥·∥ be a consistent matrix norm. Denote for each r by B(r)=[∥Cij(r)∥] an m×m matrix. The relation of the spectral radii ρ(∏r=1RC(r)) and ρ(∏r=1RB(r)) is studied in this paper. It is shown with two proofs that ρ∏r=1RC(r)⩽ρ∏r=1RB(r). Asshown in one of the proofs, ρ(∏r=1RB(r)) can be reduced so that it gives a better estimation of ρ(∏r=1RC(r)).

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