arXiv subjects

Anjali Anjali

Publications and source records attributed to Anjali Anjali.

3 recordsLinked to original sources

arXiv2026

Inner Products and Banach Algebra structures on Bicomplex Numbers and Their Associated Spaces

In this paper, we introduce various types of inner products and norms on the bicomplex number system $\mathbb{C}_2$, the bicomplex vector space ${\mathbb{C}_2}^{n}$, the space of bicomplex matrices ${C_2}^{m \times n}$, and the space of bicomplex polynomials $\mathbb{C}_2[ξ]_n$. We investigate the relationships among these inner products and norms, and establish several results. Furthermore, we prove that $\mathbb{C}_2$ and ${\mathbb{C}_2}^{n}$ are Banach algebras and Hilbert spaces. These results provide a unified framework for the study of inner product structures and normed linear spaces over bicomplex numbers and their associated spaces.

math.RT↗

arXiv2025

Idempotent & Nilpotent Operators and Matrices in Bicomplex Space

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.

math.RT↗

arXiv2025

A New Perspective on Eigenvalues and Eigenvectors of Bicomplex Linear Operators

This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems. Several theorems are explored to establish conditions for bicomplex eigenvalues and eigenvectors. Additionally, we examine the structure of the eigenspaces corresponding to these eigenvalues,analyze their properties, and discuss relevant theorems.

math.RT↗