The Drazin inverse through the matrix pencil approach and its application to the study of generalized linear systems with rectangular or square coefficient matrices.
The explicit representations of the Drazin inverses of a class of block matrices.
The inverse of the Pascal lower triangular matrix modulo .
The maximal and minimal ranks of with applications.
The minimum-norm least-squares solution of a linear system and symmetric rank-one updates.
The Moore of the Moore-Penrose inverse.
The Moore-Penrose inverse of a free matrix.
The Moore-Penrose inverse of a partitioned matrix
The Moore-Penrose inverse of a partitioned morphism in an additive category
The optimal perturbation bounds for the weighted Moore-Penrose inverse.
The quaternionic determinant.
The reciprocal super Catalan matrix
The reciprocal super Catalan matrix has entries [...] . Explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, q-analogues are also presented.
The Sherman-Morrison formula and eigenvalues of a special bordered matrix.
The singularity/nonsingularity problem for matrices satisfying diagonal dominance conditions formulated in terms of directed graphs.
The vector cross product from an algebraic point of view
The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.
Two Examples of the Bass-Quillen-Suslin Conjectures.