Ranges of Sylvester maps and a minimal rank problem.
Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix.
Rank of matrices and the Pexider equation.
Ranks and independence of solutions of the matrix equation .
Ranks of permutative matrices
A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.
Reachability matrices and cyclic matrices.
Real vector space with scalar product of quasi-triangular fuzzy numbers.
Regular positive bases
Remark on involutive subspaces and regular bases
Remark on properties of bases for additive logratio transformations of compositional data
The statistical analysis of compositional data, multivariate data when all its components are strictly positive real numbers that carry only relative information and having a simplex as the sample space, is in the state-of-the-art devoted to represent compositions in orthonormal bases with respect to the geometry on the simplex and thus provide an isometric transformation of the data to an usual linear space, where standard statistical methods can be used (e.g. [2], [4], [5], [9]). However, in some...