Idempotent & Nilpotent Operators and Matrices in Bicomplex Space

2025/06/30 by Anjali Anjali, Akhil Prakash, Anjali, Anjali +5
Mathematics · Computer Science · #Algebraic and Geometric Analysis #Matrix Theory and Algorithms #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2509.00784

Abstract

This paper explores idempotent and nilpotent operators in bicomplex spaces, focusing on their properties and behavior. We define idempotent and nilpotent matrices in this framework and derive related results. Several theorems are presented to establish conditions for the existence and behavior of bicomplex idempotent and nilpotent operators and bicomplex idempotent matrices.

Citations

• A New Perspective on Eigenvalues and Eigenvectors of Bicomplex Linear Operators
• On the Rank of a bicomplex matrix
• Matrix representations of linear transformations on bicomplex space
• Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis

Related

• Bicomplex Matrices and Operators: Jordan Forms, Invariant Subspace Lattice Diagrams, and Compact Operators
• On the Rank of a bicomplex matrix
• Matrix representations of linear transformations on bicomplex space
• A New Perspective on Eigenvalues and Eigenvectors of Bicomplex Linear Operators
• Decomposition of singular matrices into idempotents