m-applications over finite fields
Matrices which commute with a given matrix upon a subspace
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),...
Matrix rank certification.
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)...
Maximal column rank preservers of fuzzy matrices
This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.
Maximal nests of subspaces, the matrix Bruhat decomposition, and the marriage theorem---with an application to graph coloring.
Maximum rank of a power of a matrix of a given pattern
Minimal rank.
Minimal sets of vectors which generate with excess
Minimum rank of edge subdivisions of graphs.
Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.
Minimum semidefinite rank of outerplanar graphs and the tree cover number.
Mittelwertstrukturen.
Multi-covering radius for rank metric codes.