Matrix equalities and inequalities involving Khatri-Rao and Tracy-Singh sums.
Matrix equations arising in regulator problems
Matrix equivalence over finite fields
Matrix exponentials and inversion of confluent Vandermonde matrices.
Matrix field extensions
Matrix functions preserving sets of generalized nonnegative matrices.
Matrix functions: Taylor expansion, sensitivity and error analysis
Matrix identities involving multiplication and transposition
We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.
Matrix inequalities by means of embedding.
Matrix inequalities involving the Khatri-Rao product
We extend three inequalities involving the Hadamard product in three ways. First, the results are extended to any partitioned blocks Hermitian matrices. Second, the Hadamard product is replaced by the Khatri-Rao product. Third, the necessary and sufficient conditions under which equalities occur are presented. Thereby, we generalize two inequalities involving the Khatri–Rao product.
Matrix inversion and digraphs: the one factor case.
Matrix measure and application to stability of matrices and interval dynamical systems.
Matrix partitions with finitely many obstructions.
Matrix powers over finite fields.
Matrix problems and Drozd's theorem
Matrix problems and stable homotopy types of polyhedra
This is a survey of the results on stable homotopy types of polyhedra of small dimensions, mainly obtained by H.-J. Baues and the author [3, 5, 6]. The proofs are based on the technique of matrix problems (bimodule categories).
Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials
It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of . The proof...
Matrix rank and inertia formulas in the analysis of general linear models
Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and establishing equalities and inequalities occurred in statistical analysis. This paper describes how to establish exact formulas for calculating ranks and inertias of covariances of predictors and estimators of parameter spaces in general linear models (GLMs),...
Matrix rank certification.
Matrix rank/inertia formulas for least-squares solutions with statistical applications
Least-Squares Solution (LSS) of a linear matrix equation and Ordinary Least-Squares Estimator (OLSE) of unknown parameters in a general linear model are two standard algebraical methods in computational mathematics and regression analysis. Assume that a symmetric quadratic matrix-valued function Φ(Z) = Q − ZPZ0 is given, where Z is taken as the LSS of the linear matrix equation AZ = B. In this paper, we establish a group of formulas for calculating maximum and minimum ranks and inertias of Φ(Z)...