On a question concerning condition numbers for Markov chains

Let S be an irreducible stochastic matrix of order n with left stationary vector pi(T), and let S-(i) denote the principal submatrix of S formed by deleting the ith row and column. We prove that max(1less than or equal toiless than or equal ton) piiparallel to(I-S-(i))(-1)parallel to(infinity)<min(1less than or equal tojless than or equal ton) parallel to(I-S-(j))(-1)parallel to(infinity), thus answering question posed by Cho and Meyer. We provide an attainable lower bound on max(1less than or equal toiless than or equal ton) piiparallel to(I-S-(i))(-1)parallel to(infinity), and discuss the case that equality holds in that bound.