Related papers: Hartwig-Spindelb\"ock decomposition of dual comple…
In this paper, we introduce two new forms of the dual Hartwig-Spindelb{\"o}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further…
In this work, we introduce a new type of generalized inverse called dual core-EP generalized inverse (in short DCEPGI) for dual square matrices. We analyze the existence and uniqueness of the DCEPGI inverse and its compact formula using…
In this paper, we introduce the dual $r$-rank decomposition of dual matrix, get its existence condition and equivalent form of the decomposition, as well as derive some characterizations of dual Moore-Penrose generalized inverse(DMPGI).…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.
In this paper we introduce the generalized inverse of complex square matrix with respect to other matrix having same size. Some of its representations, properties and characterizations are obtained. Also some new representation matrices of…
This paper uses matrix transformations to provide the Autoone-Takagi decomposition of dual complex symmetric matrices and extends it to dual quaternion $\eta$-Hermitian matrices. The LU decomposition of dual matrices is given using the…
We introduce right eigenvalues and subeigenvalues for square dual complex matrices. An $n \times n$ dual complex Hermitian matrix has exactly $n$ right eigenvalues and subeigenvalues, which are all real. The Hermitian matrix is positive…
We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…
An arbitrary Mueller matrix can be decomposed into a sum of up to four deterministic Mueller-Jones matrices, with strengths given by the eigenvalues of an associated Hermitian matrix. A geometrical representation of the eigenvalues in terms…
A new generalized inverse for a square matrix $H\in\mathbb{C}^{n\times n}$, called CCE-inverse, is established by the core-EP decomposition and Moore-Penrose inverse $H^{\dag}$. We propose some characterizations of the CCE-inverse.…
The main objective of this paper is to introduce unique representations and characterizations for the weighted core inverse of matrices. We also investigate various properties of these inverses and their relationships with other generalized…
In this paper, we introduce the notion of the core-EP decomposition and some of its properties. By using the decomposition, we derive several characterizations of the core-EP inverse, introduce a pre-order(i.e. the core-EP order) and a…
We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for…
Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…
In this paper Witten type deformation of osp(1/2) algbera is introduced and its realization and matrix representation are obtained. The matrix representation is shown to be possible only when the dimension is odd.
We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.
The idea of decomposing a matrix into a product of structured matrices such as triangular, orthogonal, diagonal matrices is a milestone of numerical computations. In this paper, we describe six new classes of matrix decompositions,…
We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…
Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of…
We give a decomposition as a direct sum of indecomposable modules of several types of Specht modules in characteristic $2$. These include the Specht modules labelled by hooks, whose decomposability was considered by Murphy. Since the main…