On the singular decomposition of matrices.
Operator matrix of Moore-Penrose inverse operators on Hilbert C*-modules
We show that the Moore-Penrose inverse of an operator T is idempotent if and only if it is a product of two projections. Furthermore, if P and Q are two projections, we find a relation between the entries of the associated operator matrix of PQ and the entries of associated operator matrix of the Moore-Penrose inverse of PQ in a certain orthogonal decomposition of Hilbert C*-modules.
Optimal design in small amplitude homogenization
This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide...
Orthogonalization, factorization, and identification as to the theory of recursive equations in linear algebra.
Pairs of k -step reachability and m -step observability matrices
Let V and W be matrices of size n × pk and qm × n, respectively. A necessary and sufficient condition is given for the existence of a triple (A,B,C) such that V a k-step reachability matrix of (A,B) andW an m-step observability matrix of (A,C).
Parallel and superfast algorithms for Hankel systems of equations.
Partial isometries and EP elements in rings with involution.
Perturbation of the generalized Drazin inverse.
Positive splittings of matrices and their nonnegative Moore-Penrose inverses
In this short note we study necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a real matrix in terms of certain spectral property shared by all positive splittings of the given matrix.
Power bounded and exponentially bounded matrices
The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.
Prediction for Two Processes and the Nehari Problem.
Product of range symmetric block matrices in Minkowski space.
Propriétés des matrices «bien localisées» près de leur diagonale et quelques applications
Pseudoblock conditions of diagonal dominance.
Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem.
Pseudo-similarity and partial unit regularity
Range symmetric matrices in Minkowski space.
Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix.
Ranks and independence of solutions of the matrix equation .
Regular Splittings and the Discrete Neumann Problem.