Low-rank iterative methods for projected generalized Lyapunov equations.
Mathematical basis of a system supporting interconnection design.
Matrices over centrally -graded rings.
Matrices which commute with a given matrix upon a subspace
Matrix bounds for the solution of the continuous algebraic Riccati equation.
Matrix divisors of mI
Matrix equations arising in regulator problems
Matrix equivalence over finite fields
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 powers over finite fields.
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/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)...
Matrix transformations and quasi-Newton methods.
Maximal invariant neutral subspaces and an application to the algebraic Riccati equation.
Maximal solutions of two–sided linear systems in max–min algebra
Max-min algebra and its various aspects have been intensively studied by many authors [1, 4] because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations , with given coefficient matrices and . We present a polynomial method for...
Maximizing the determinant for a special class of block-partitioned matrices.
Multiplicative maps that are close to an automorphism on algebras of linear transformations
Let be a complex, separable Hilbert space of finite or infinite dimension, and let ℬ() be the algebra of all bounded operators on . It is shown that if φ: ℬ() → ℬ() is a multiplicative map(not assumed linear) and if φ is sufficiently close to a linear automorphism of ℬ() in some uniform sense, then it is actually an automorphism; as such, there is an invertible operator S in ℬ() such that for all A in ℬ(). When is finite-dimensional, similar results are obtained with the mere assumption that there...
Necessary and sufficient conditions for the existence of a Hermitian positive definite solution of a type of nonlinear matrix equations.
Negative powers and the spectrum of matrices
New estimates for the solution of the Lyapunov matrix differential equation.