Jordan chains of $h$-cyclic matrices

TL;DR

This paper investigates the Jordan chains of $h$-cyclic matrices, providing new theoretical insights and auxiliary results relevant to nonnegative imprimitive irreducible matrices, supported by illustrative examples.

Contribution

It introduces novel results on Jordan chains of $h$-cyclic matrices and extends these findings to nonnegative imprimitive irreducible matrices.

Findings

Characterization of Jordan chains for $h$-cyclic matrices

Auxiliary results for nonnegative imprimitive irreducible matrices

Illustrative examples demonstrating theoretical results

Abstract

Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an $h$-cyclic matrix. We also present ancillary results applicable to nonnegative imprimitive irreducible matrices and demonstrate these results via examples.