Rank Of bicomplex matrices and system of algebraic equations

2025/05/18 by Amita, Amita, Prakash, Akhil, Wagh, Mamta Amol +1
#15A03 #15A04 #15A24 #15A30 (Primary) 30G35 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2505.12295

Abstract

In this paper, we study the rank of matrices of bicomplex numbers. The relationship between rank, idempotent column rank and idempotent row rank is examined. Then, the solution of a system of equations in bicomplex space is presented using a new technique. Moreover, we establish a necessary and sufficient condition for the existence of solutions of a system of equations in bicomplex space and derive some related results.

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

• On the Rank of a bicomplex matrix
• Bounds for the zeros of Bicomplex Polynomials using matrix method
• Solution Theory for Systems of Bilinear Equations
• Idempotent & Nilpotent Operators and Matrices in Bicomplex Space
• Polynomial Equations and Rank of Matrices Over F₂ Related to Persymmetric Matrices