On the Rank of a bicomplex matrix

TL;DR

This paper investigates the rank properties of bicomplex matrices, examining four types of ranks, their equivalences, and introduces the concepts of idempotent row and column spaces with illustrative examples.

Contribution

It introduces and analyzes four types of ranks for bicomplex matrices and explores conditions for their equivalence, along with defining idempotent row and column spaces.

Findings

Identified conditions under which different rank types are equivalent

Defined and studied idempotent row and column spaces of bicomplex matrices

Provided examples and counterexamples to illustrate the concepts

Abstract

The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row space and idempotent column space of a bicomplex matrix. Some examples and counter examples have been presented to substantiate the study.