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Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures

Zygmunt M. J.

Opuscula Mathematica

2016

Vol. 36, no. 3

409--423

The paper focuses on matrix-valued polynomials satisfying a three-term recurrence relation with constant matrix coefficients. It is shown that they form an orthogonal system with respect to a matrix of measures, not necessarily symmetric. Moreover, it is stated the condition on the coefficients of the recurrence formula for which the matrix measure is symmetric.

Non symmetric random walk on infinite graph

Zygmunt M. J.

Opuscula Mathematica

2011

Vol. 31, no. 4

669-674

We investigate properties of a non symmetric Markov's chain on an infinite graph. We show the connection with matrix valued random walk polynomials which satisfy the orthogonality formula with respect to non a symmetric matrix valued measure.