An additive inverse characteristic polynomial theorem
An algebra of abstract vector variables.
An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.
In this paper we show that in an analogous way to the scalar case, the general solution of a non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions of certain matrices related to the corresponding characteristic algebraic matrix equation. We introduce the concept of co-solution of an algebraic equation of the type X^2 + A1.X + A0 = 0, that allows us to obtain a method of the variation of the parameters for the matrix case and further to find...
An algebraic construction of discrete wavelet transforms
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
An algorithm for determining if the inverse of a strictly diagonally dominant Stieltjes matrix is strictly ultrametric.
An Algorithm for Scaling Matrices and Computing the Minimum Cycle Mean in a Digraph.
An algorithm for solving the absolute value equation.
An algorithm for the inversion of partitioned matrices
An algorithm that carries a square matrix into its transpose by an involutory congruence transformation.
An alternative approach to characterize the commutativity of orthogonal projectors
In an invited paper, Baksalary [Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors. In: T. Pukkila, S. Puntanen (Eds.), Proceedings of the Second International Tampere Conference in Statistics, University of Tampere, Tampere, Finland, [2], pp. 113-142] presented 45 necessary and sufficient conditions for the commutativity of a pair of orthogonal projectors. Basing on these results, he discussed therein also statistical aspects of the commutativity...
An Alternative Givens Ordering.
An analysis of GCD and LCM matrices via the -factorization.
An analytical approach to Cayley-Hamilton theorem
Cayley-Hamilton theorem is proved by an analytical approach by recalling certain interesting properties of density. In this process, the classical expressions of the principal invariants follow immediately from the proposed proof's scheme.
An angle metric through the notion of Grassmann representative.
An application of Halls' theorems to matrices
An Application of -K-Theory to the Global Analysis of Matrix Valued Functions.
An application of matrix calculus to an engineering problem.
An approach based on matrix polynomials for linear systems of partial differential equations
In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method...
An easily computable invariant of trilinear alternating forms
An efficient algorithm for computing real powers of a matrix and a related matrix function
The paper is devoted to an algorithm for computing matrices and for a given square matrix and a real . The algorithm uses the binary expansion of and has the logarithmic computational complexity with respect to . The problem stems from the control theory.