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Partial norms and the convergence of general products of matrices - MaRDI portal

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Partial norms and the convergence of general products of matrices

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Publication:6503690

arXivmath/9802108MaRDI QIDQ6503690

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Abstract: Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from a sequence of real or complex matrices. When the matrices have a common invariant subspace H, we give a sufficient condition for the convergence to 0 on H of a general product. Our result is applied to obtain a condition for the weak ergodicity of an inhomogeneous Markov chain. We compare various types of contractions which may be defined for a single matrix, such as paracontraction, l--contraction, and H--contraction, where H is an invariant subspace of the matrix.





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