On classification of normal matrices in indefinite inner product spaces.
On (con)similarities and congruences between and , or .
On convexity of polynomial paths and generalized majorizations.
On corepresentations of equipped posets and their differentiation.
On Kolchin's theorem.
A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent.Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite dimensional algebra...
On -estimates for hyperbolic systems
On linear preservers of two-sided gut-majorization on
For it is said that is gut-majorized by , and we write , if there exists an -by- upper triangular g-row stochastic matrix such that . Define the relation as follows. if is gut-majorized by and is gut-majorized by . The (strong) linear preservers of on and strong linear preservers of this relation on have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of on and .
On Neighbouring Matrices with Quadratic Elementary Divisors.
On polynomial invariant chains of matrices and principal submatrices
On reducing and deflating subspaces of matrices.
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 S-Equivalence of Seifert Matrices.
On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems.
On the decoupling of one class of multivariable systems
On the Degree of the Minimal Polynomial of the Lyapunov Operator.
On the diagonalisation of von Neumann regular matrices
On the diagonals of integral matrices
On the doubling of quadratic algebras
The concept of doubling, which was introduced around 1840 by Graves and Hamilton, associates with any quadratic algebra 𝓐 over a field k of characteristic not 2 its double 𝓥(𝓐 ) = 𝓐 × 𝓐 with multiplication (w,x)(y,z) = (wy - z̅x,xy̅ + zw). This yields an endofunctor on the category of all quadratic k-algebras which is faithful but not full. We study in which respect the division property of a quadratic k-algebra is preserved under doubling and, provided this is the case, whether the...
On the finiteness of the semigroup of conjugacy classes of left ideals for algebras with radical square zero
Let A be a finite-dimensional algebra over an algebraically closed field with radical square zero, and such that all simple A-modules have dimension at most two. We give a characterization of those A that have finitely many conjugacy classes of left ideals.
On the invariant factors of sums of integral matrices