On some classes of linear equations.
On some classes of linear equations, II.
On some free semigroups, generated by matrices
Let We call a complex number “semigroup free“ if the semigroup generated by and is free and “free” if the group generated by and is free. First families of semigroup free ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free ’s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common picture....
On some generalizations of the Vandermonde matrix and their relations with the Euler beta-function.
On some Generalized Inverses of Matrices and some Linear Matrix Equations
On some identities involving spherical means
For every positive definite quadratic form in variables the reciprocal of the square root of the discriminant is equal to the arithmetic mean of the values assumed by the form on the sphere centered at and with radius raised to the ()-th. power. Various consequences are deduced from this, in particular a simplification of some calculations from which one obtains the possibility of solving linear systems using spherical means rather than determinants.
On some matrix trace inequalities.
On Some new Inclusion Theorems for the Eigenvalues of Partitioned Matrices.
On some problem related to fundamental cycle sets of a graph: Research notes
On some representations of hypergroups
On some spectral characteristics of multiparameter polynomial matrices.
On spaces of matrices with a bounded number of eigenvalues.
On sparsity of approximate solutions to max-plus linear systems
When a system of one-sided max-plus linear equations is inconsistent, the approximate solutions within an admissible error bound may be desired instead, particularly with some sparsity property. It is demonstrated in this paper that obtaining the sparsest approximate solution within a given error bound may be transformed in polynomial time into the set covering problem, which is known to be NP-hard. Besides, the problem of obtaining the sparsest approximate solution within a given error bound...
On spectra of expansion graphs and matrix polynomials. II.
On spectra perturbation and elementary divisors of positive matrices.
On spectral properties of linear combinations of idempotents
Let P,Q be two linear idempotents on a Banach space. We show that the closedness of the range and complementarity of the kernel (range) of linear combinations of P and Q are independent of the choice of coefficients. This generalizes known results and shows that many spectral properties of linear combinations do not depend on their coefficients.
On spectral variations under bounded real matrix perturbations.
On spinor varieties and their secants.
On stability of parametrized families of polynomials and matrices.
On submultiplicative nonnegative functionals on linear maps of linear finitedimensional normed spaces