A NOTE ON EIGENVALUES OF BICOMPLEX MATRIX (original) (raw)

DIAGONALIZATION OF THE BICOMPLEX MATRIX

International Journal of Research Publication and Reviews (IJRPR), 2022

In this paper, we have studied and investigated the properties of bicomplex matrices. On invertible and non-invertible bicomplex matrices, we have obtained certain results. The bicomplex matrix's eigenvalues, eigenvectors and spectrum are also introduced. For bicomplex matrices, the Cayley-Hamilton theorem has been investigated. Furthermore, we discussed the Diagonalizable Bicomplex matrix along with certain results.

On Some Properties of Determinants of Bicomplex Matrices

In this paper, we have studied Determinants of Bicomplex Matrices and investigated their properties. We have introduced Bicomplex Symmetric Matrix, Bicomplex Skew-Symmetric Matrix, Bicomplex idempotent matrix, Bicomplex Skew-idempotent matrix, Bicomplex Involutory matrix, Bicomplex skew-involutory matrix, three types of Hermetian and Skew-Hermetian Matrix, Bicomplex Orthogonal Matrix and three types of Unitary Matrix and investigated the properties of their determinants.

ON SOME PROPERTIES OF DETERMINANTS OF BICOMPLEX MATRICES JSTR

Journal of Science and Technological Researches, 2022

In this paper, we have studied determinants of bicomplex matrices and investigated their properties. We have introduced bicomplex symmetric matrix, bicomplex skew-symmetric matrix, bicomplex idempotent matrix, bicomplex skew-idempotent matrix, bicomplex involutory matrix, bicomplex skew-involutory matrix, three types of Hermetian and skew-Hermetian matrix, bicomplex orthogonal matrix and three types of unitary matrix and investigated the properties of their determinants. 2010 AMS Subject Classification. 30G35, 32A30, 32A10, 15A15, 15B57, 15B10, 15A18. Keywords: Bicomplex matrix, determinant of bicomplex matrix, orthogonal matrix, unitary matrix.

Certain Results on Bicomplex Matrices By Anjali & Amita

Global Journal of Science Frontier Research, 2018

This paper begins the study of bicomplex matrices. In this paper, we have defined bicomplex matrices, determinant of a bicomplex square matrix and singular and non-singular matrices in C 2. We have proved that the set of all bicomplex square matrices of order n is an algebra. We have given some definitions and results regarding adjoint and inverse of a matrix in C 2. We have defined three types of conjugates and three types of tranjugates of a bicomplex matrix. With the help of these conjugates and tranjugates, we have also defined symmetric and skew-symmetric matrices, Hermitian and Skew-Hermitian matrices in C 2 .

On Some Matrix Representations of Bicomplex Numbers

2019

In this work, we have defined bicomplex numbers whose coefficients are from the Fibonacci sequence. We examined the matrix representations and algebraic properties of these numbers. We also computed the eigenvalues and eigenvectors of these particular matrices.

Bicomplex Version of Cayley Hamilton Theorem

Theory of matrices is an integral part of algebra as well as Theory of equations. Matrices plays an important role in every branch of Physics, Computer Graphics and are also used in representing the real world's data and there are so many applications of matrices ,for this reason we thought of studying bicomplex matrices. The monograph by Price [4] contains few exercises pertaining to matrices with bicomplex entries. In this paper we discussed the bicomplex version of CAYLEY – HAMILTON THEOREM and also used it to evaluate the inverse of a non singular bicomplex matrix.

A note on Bicomplex Linear operators on bicomplex Hilbert spaces

International Journal of Mathematics Trends and Technology, 2016

In this paper we define the isomorphism between the bicomplex Hilbert spaces. We also give some simple and basic results on bicomplex isomorphism with respect to hyperbolic-valued norm on the bicomplex Hilbert spaces.

A New Approach to Bicomplex Jacobsthal Matrix and Bicomplex Jacobsthal-Lucas Matrix Components

Journal of Advances in Mathematics and Computer Science

In this present paper, we give a detailed study of a new generation of Bicomplex Jacobsthal matrix and Bicomplex Jacobsthal-Lucas matrix using Jacobsthal -matrix and Jacobsthal Lucas -matrix. Also presented some formulas, facts, and properties about these matrices. In addition, a new vector called the bicomple Jacobsthalvectors and the bicomplex Jacobsthal-Lucas vectors with matrix components is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of space. Then, using this matrix representation, we give some identities.

The Real Matrices forms of the Bicomplex Numbers and Homothetic Exponential motions

2014

In this paper, a bicomplex number is described in four- dimensional space and its a variety of algebraic properties is presented. In addition, Pauli-spin matrix elements corresponding to base the real matrices forms of the bicomplex numbers are obtained and its the algebraic properties are given. Like i and j in two different spaces are defined terms of Euler's formula. In the last section velocities become higher order by giving an exponential homothetic motion for the bicomplex numbers. And then, Due to the way in which the matter is presented, the paper gives some formula and facts about exponential homothetic motions which are not generally known