An Estimation of the Spectral Radius of a Product of Block Matrices
Linear Algebra and Its Applications
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)).
Chen, Mei-Qin, Xiezhang Li.
"An Estimation of the Spectral Radius of a Product of Block Matrices."
Linear Algebra and Its Applications, 379: 267-275.
doi: 10.1016/S0024-3795(03)00545-7 source: https://www.sciencedirect.com/science/article/pii/S0024379503005457?via%3Dihub