Note on the core matrix partial ordering
Complementing the work of Baksalary and Trenkler [2], we announce some results characterizing the core matrix partial ordering.
Notice on the Chipman generalization of the matrix inverse
Numerical Solution of Linear Equations with Toeplitz and Vector Toeplitz Matrices.
On a bound on algebraic connectivity: the case of equality
In a recent paper the authors proposed a lower bound on , where , , is an eigenvalue of a transition matrix of an ergodic Markov chain. The bound, which involved the group inverse of , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...
On a group of mixed-type reverse-order laws for generalized inverses of a triple matrix product with applications.
On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems.
On a Schur complement inequality for the Hadamard product of certain totally nonnegative matrices.
On a System of Functional Equations
On block triangular matrices with signed Drazin inverse
The sign pattern of a real matrix , denoted by , is the -matrix obtained from by replacing each entry by its sign. Let denote the set of all real matrices such that . For a square real matrix , the Drazin inverse of is the unique real matrix such that , and , where is the Drazin index of . We say that has signed Drazin inverse if for any , where denotes the Drazin inverse of . In this paper, we give necessary conditions for some block triangular matrices to have signed...
On commuting generalized inverses in semigroups.
On commuting generalized inverses of matrices and in associative rings.
On Davis-Kahan-weinberger Extension Theorem
On generalized inverses of banded matrices.
On inverses of triangular matrices with monotone entries.
On Inverses of Vandermonde and Confluent Vandermonde Matrices III.
On linear operators strongly preserving invariants of Boolean matrices
Let be the general Boolean algebra and a linear operator on . If for any in (, respectively), is regular (invertible, respectively) if and only if is regular (invertible, respectively), then is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over . Meanwhile, noting that a general Boolean algebra is isomorphic...
On matrices with all minors negative.
On matrix convexity of the Moore-Penrose inverse.
On melancholic magic squares
Starting with Dürer's magic square which appears in the well-known copper plate engraving Melencolia we consider the class of melancholic magic squares. Each member of this class exhibits the same 86 patterns of Dürer's magic square and is magic again. Special attention is paid to the eigenstructure of melancholic magic squares, their group inverse and their Moore-Penrose inverse. It is seen how the patterns of the original Dürer square to a large extent are passed down also to the inverses of the...
On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product.