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.
On the linear capacity of algebraic cones
We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of the Matrix Theory. We derive in an explicit way the formula for the linear capacity of an irreducible component of the zero cone of a quadratic form over an algebraically closed field. We also give a formula for the linear capacity of the cone over the conjugacy class of a “generic” non-nilpotent matrix.
On the minimum rank of not necessarily symmetric matrices: a preliminary study.
On the reduction of a random basis
For p ≤ n, let b1(n),...,bp(n) be independent random vectors in with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...
On the shortest lattice vectors in a three-dimensional translational (Bravais) lattice
Optimal subspaces and constrained principal component analysis.
Ordered structures and projections.