Matrices over centrally -graded rings.
Matrix exponentials and inversion of confluent Vandermonde matrices.
Matrix inversion and digraphs: the one factor case.
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),...
Minimization of constrained quadratic forms in Hilbert spaces.
Mixed-type reverse order law and its equivalents
We present new results related to various equivalents of the mixed-type reverse order law for the Moore-Penrose inverse for operators on Hilbert spaces. Recent finite-dimensional results of Tian are extended to Hilbert space operators.
Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix
By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases. By a centered symmetric matrix we mean a symmetric matrix with zero row (and hence column) sums. There is a one-toone correspondence between the classes of hollow symmetric matrices and centered symmetric matrices, and thus with any hollow symmetric matrix D we may associate a centered symmetric matrix B, and vice...
Moore-Penrose inverse, parabolic subgroups, and Jordan pairs.
Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space
In this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using the indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of certain closed convex cones.
Moore-Penrose inverses of Gram operators on Hilbert C*-modules
Let t be a regular operator between Hilbert C*-modules and be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator t*t. More precisely, we study some conditions ensuring that and . As an application, we get some results for densely defined closed operators on Hilbert C*-modules over C*-algebras of compact operators.