On a group of mixed-type reverse-order laws for generalized inverses of a triple matrix product with applications.
On certain non-constructive properties of infinite-dimensional vector spaces
In set theory without the axiom of choice (), we study certain non-constructive properties of infinite-dimensional vector spaces. Among several results, we establish the following: (i) None of the principles AC (AC for linearly ordered families of nonempty sets)—and hence AC (AC for well-ordered families of nonempty sets)— (where is an uncountable regular cardinal), and “for every infinite set , there is a bijection ”, implies the statement “there exists a field such that every vector...
On generalized inverses of banded matrices.
On infinite bounded-Toeplitz extensions of Toeplitz matrices.
On Konieczny's conjecture of Boolean matrices.
On low rank perturbations of complex matrices and some discrete metric spaces.
On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product.
On rank one matrices and invariant subspaces.
On rank subtractivity between normal matrices.
On sequences not enjoying Schur’s property
Here we proved the existence of a closed vector space of sequences - any nonzero element of which does not comply with Schur’s property, that is, it is weakly convergent but not norm convergent. This allows us to find similar algebraic structures in some subsets of functions.
On sets of vectors of a finite vector space in which every subset of basis size is a basis
It is shown that the maximum size of a set of vectors of a -dimensional vector space over , with the property that every subset of size is a basis, is at most , if , and at most , if , where and is prime. Moreover, for , the sets of maximum size are classified, generalising Beniamino Segre’s “arc is a conic” theorem. These results have various implications. One such implication is that a matrix, with and entries from , has columns which are linearly dependent. Another is...
On solutions to the quaternion matrix equation .
On Some Classes Of Linear Equations
On some classes of linear equations.
On some classes of linear equations, II.
On some problem related to fundamental cycle sets of a graph: Research notes
On spaces of matrices with a bounded number of eigenvalues.
On the algebraic properties of convex bodies and some applications.
On the angles between certain arithmetically defined subspaces of
If and are two families of unitary bases for , and is a fixed number, let and be subspaces of spanned by vectors in and respectively. We study the angle between and as goes to infinity. We show that when and arise in certain arithmetically defined families, the angles between and may either tend to or be bounded away from zero, depending on the behavior of an associated eigenvalue problem.
On the belonging of a perturbed vector to a subspace from a numerical view point.