Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.
Fast Givens transformation for quaternion valued matrices applied to Hessenberg reductions.
Fermat's theorem for matrices revisited
First order linear ordinary differential equations in associative algebras.
Gauss sums and the matrix equation over fields of characteristic two
Gauss sums and the number of solutions to the matrix equation over
Generalized equivalence of matrices over Prüfer domains.
Group inverse for the block matrix with two identical subblocks over skew fields.
Growth in
Hamiltonian square roots of skew Hamiltonian quaternionic matrices.
Hidden relations for the Smith invariants of a matrix sum
How to establish universal block-matrix factorizations.
Idempotent and compact matrices on linear lattices: A survey of some lattice results and related solutions of finite relational equations.
Indecomposable matrices over a distributive lattice
In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set of all fully indecomposable matrices as a subsemigroup of the semigroup of all Hall matrices over the lattice are given.
Integer sequences and matrices over finite fields.
Invertible commutativity preservers of matrices over max algebra
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra.
Investigating generalized quaternions with dual-generalized complex numbers
We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values , and . Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given.
Involutions and semiinvolutions
We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.
Isotropic subspaces for pairs of Hermitian matrices.
Left eigenvalues of symplectic matrices.