On rank one matrices and invariant subspaces.
On rank subtractivity between normal matrices.
On realizability of p-groups as Galois groups
2000 Mathematics Subject Classification: 12F12, 15A66.In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related topics.
On reducing and deflating subspaces of matrices.
On regular elements in an incline.
On relations between right and left eigenvectors of nonselfadjoint matrix pencils
On relations of invariants for vector-valued forms.
On Roth's pseudo equivalence over rings.
On row-sum majorization
Let be the set of all real or complex matrices. For , we say that is row-sum majorized by (written as ) if , where is the row sum vector of and is the classical majorization on . In the present paper, the structure of all linear operators preserving or strongly preserving row-sum majorization is characterized. Also we consider the concepts of even and circulant majorization on and then find the linear preservers of row-sum majorization of these relations on .
On SAP Fields.
On separation of eigenvalues by the permutation group
Let A be an invertible 3 × 3 complex matrix. It is shown that there is a 3 × 3 permutation matrix P such that the product PA has at least two distinct eigenvalues. The nilpotent complex n × n matrices A for which the products PA with all symmetric matrices P have a single spectrum are determined. It is shown that for a n × n complex matrix [...] there exists a permutation matrix P such that the product PA has at least two distinct eigenvalues.
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 S-Equivalence of Seifert Matrices.
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 several matrix Kantorovich-type inequalities.
On solution sets of information inequalities
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
On solutions of a matrix equations system AX = B, XD = E
On solutions to the quaternion matrix equation .
On some algebraic identities and the exterior product of double forms
We use the exterior product of double forms to free from coordinates celebrated classical results of linear algebra about matrices and bilinear forms namely Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and Jacobi’s formula for the determinant. This coordinate free formalism is then used to easily generalize the previous results to higher multilinear forms namely to double forms. In particular, we show that the Cayley-Hamilton theorem once applied to the second...
On Some Classes Of Linear Equations