Cycles of linear and semilinear mappings

TL;DR

This paper introduces a canonical form for matrices representing cycles of linear and semilinear mappings between complex vector spaces, providing a unified framework for their classification.

Contribution

It presents a new canonical form for cycles of linear and semilinear mappings, extending previous classification methods to these structures.

Findings

Canonical form for cycles of linear and semilinear mappings established

Unified approach for classifying such cycles demonstrated

Framework applicable to complex vector space mappings

Abstract

We give a canonical form of matrices of a cycle of linear or semilinear mapping V_1 --- V_2 --- ... --- V_t --- V_1 in which all V_i are complex vector spaces, each line is an arrow ---> or <---, and each arrow denotes a linear or semilinear mapping.