Related papers: Non-reproductive and reproductive solutions of som…
In this paper we analyse Cline's matrix equation, generalized Penrose's matrix system and a matrix system for k-commutative {1}-inverses. We determine reproductive and non-reproductive general solutions of analysed matrix equation and…
In this article we consider a consistent matrix equation $AXB = C$ when a particular solution $X_{0}$ is given and we represent a new form of the general solution which contains both reproductive and non-reproductive solutions (it depends…
In this paper we represent a new form of condition for the consistency of the matrix equation AXB=C. If the matrix equation AXB=C is consistent, we determine a form of general solution which contains both reproductive and non-reproductive…
By a generalized inverse of a given matrix, we mean a matrix that exists for a larger class of matrices than the nonsingular matrices, that has some of the properties of the usual inverse, and that agrees with inverse when given matrix…
Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing…
One of the fundamental research problems in the theory of generalized inverses of matrices is to establish reverse order laws for generalized inverses of matrix products. Under the assumption that $A$, $B$, and $C$ are three nonsingular…
This paper deals with necessary and sufficient condition for consistency of the matrix equation $AXB = C$. We will be concerned with the minimal number of free parameters in Penrose's formula $X = A^(1)CB^(1) + Y - A^(1)AYBB^(1)$ for…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their…
Some inverse problems for semi-infinite periodic generalized Jacobi matrices are considered. In particular, a generalization of the Abel criterion is presented. The approach is based on the fact that the solvability of the Pell-Abel…
Explicit details are presented for calculation of $A^+B$, $A^+AB$ and $AA^+B$ where $A_{m\times n}$ is any nonzero matrix, $A^+$ is the Moore-Penrose pseudoinverse of $A$ and $B$ is any matrix of appropriate dimensions, where the quantities…
We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into…
In this paper we will consider Rohde's general form of {1}-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free…
This paper gives three formulas for the pseudoinverse of a matrix product $A = CR$. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse $A^+_r$ may be…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the…
The Drazin inverse solutions of the matrix equations ${\rm {\bf A}}{\rm {\bf X}} = {\rm {\bf B}}$, ${\rm {\bf X}}{\rm {\bf A}} = {\rm {\bf B}}$ and ${\rm {\bf A}}{\rm {\bf X}}{\rm {\bf B}} ={\rm {\bf D}} $ are considered in this paper. We…
In this paper, the consimilarity of complex matrices is generalized for the split quaternions. In this regard, coneigenvalue and coneigenvector are defined for split quaternion matrices. Also, the existence of solution to the split…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a damped Newton--Schulz (NS) iteration tailored to…