Schur complements of matrices with acyclic bipartite graphs.
Smooth factorizations of matrix valued functions and their derivatives.
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 characterizations of totally nonpositive (totally negative) matrices.
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 factorizations of matrix functions in several variables
We establish some criteria for a nonsingular square matrix depending on several parameters to be represented in the form of a matrix product of factors which depend on the single parameters.
Special Similarity Transformations in Connection with the Quadrant Interlocking Factorisation Techniques
Stability and sensivity of Darboux transformation without parameter.