Schur complements and Banachiewicz-Schur forms.
Schur complements of matrices with acyclic bipartite graphs.
Self-correcting iterative methods for computing -inverses
In this paper we construct a few iterative processes for computing -inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.
Sign patterns that require a positive or nonnegative left inverse.
Singular M-matrices which may not have a nonnegative generalized inverse
A matrix A ∈ ℝn×n is a GM-matrix if A = sI − B, where 0 < ρ(B) ≤ s and B ∈WPFn i.e., both B and Bt have ρ(B) as their eigenvalues and their corresponding eigenvector is entry wise nonnegative. In this article, we consider a generalization of a subclass of GM-matrices having a nonnegative core nilpotent decomposition and prove a characterization result for such matrices. Also, we study various notions of splitting of matrices from this new class and obtain sufficient conditions for their convergence....
Solutions of minus partial ordering equations over von Neumann regular rings
In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.
Solvability classes for core problems in matrix total least squares minimization
Linear matrix approximation problems are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...
Some algebraic and statistical properties of WLSEs under a general growth curve model.
Some considerations of matrix equations using the concept of reproductivity
Some equalities for generalized inverses of matrix sums and block circulant matrices
Let be complex matrices of the same size. We show in this note that the Moore-Penrose inverse, the Drazin inverse and the weighted Moore-Penrose inverse of the sum can all be determined by the block circulant matrix generated by . In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.
Some remarks on generalized inverses of conjugate EP matrix.
Some remarks on possible generalized inverses in semigroups.
Some results on matrix partial orderings and reverse order law.
Some results on the group inverse for block matrices over skew fields.
Special forms of generalized inverses of row block matrices.
Spectrum of infinite block matrices and -triangular operators.
Strict spectral approximation of a matrix and some related problems
We show how the strict spectral approximation can be used to obtain characterizations and properties of solutions of some problems in the linear space of matrices. Namely, we deal with (i) approximation problems with singular values preserving functions, (ii) the Moore-Penrose generalized inverse. Some properties of approximation by positive semi-definite matrices are commented.
Structured condition numbers and backward errors in scalar product spaces.
Stupeň inverznej krivky v projektívnom priestore Lagrangeových-Sylvestrových polynómov
Subdirect sums of nonsingular -matrices and of their inverses.