From equivalent linear equations to Gauss-Markov theorem.
Gauss sums and the matrix equation over fields of characteristic two
Gauss sums and the number of solutions to the matrix equation over
Generalized Green's functions for higher order boundary value matrix differential systems.
Generalized Matrices
Generalized Schröder matrices arising from enumeration of lattice paths
We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps , , , and and not going above the line . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition,...
Green's relations for stochastic matrices
Hamiltonian square roots of skew Hamiltonian quaternionic matrices.
Hermitian nonnegative-definite and positive-definite solutions of the matrix equation .
Hypersymmetric functions and Pochhammers of nonautonomous matrices.
Idempotent and compact matrices on linear lattices: A survey of some lattice results and related solutions of finite relational equations.
Indecomposable parabolic bundles
We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of conjugacy classes of n×n matrices for which one can find matrices in their closures whose product is equal to the identity matrix. Both answers depend on the root system of a Kac-Moody Lie algebra. Our proofs use Ringel’s theory of tubular algebras, work of Mihai on the existence of logarithmic connections, the Riemann-Hilbert...
Inertias and ranks of some Hermitian matrix functions with applications
Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively. As applications,...
Invariance of recurrence sequences under a Galois group.
Invariance properties of an operator product involving generalized inverses.
-spectral factorization for rational matrix functions with alternative realization.
Jordan Chains for Lambda Matrices, II.
Least squares (P,Q)-orthogonal symmetric solutions of the matrix equation and its optimal approximation.
Linear fractional transformations and companion matrices
Linearization of regular matrix polynomials.