Ein Algorithmus zur zyklisch invarianten Zerlegung eines endlich-dimensionalen Vektorraums bezüglich einer linearen Selbstabbildung.
Embedding properties of endomorphism semigroups
Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by Sub V (resp., End V) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply the following: (1) If card Ω ≥ 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff . In particular, if Ω has at least two elements, then there exists no semigroup embedding from Self Ω into the dual of PSelf Ω. (2) If V is infinite-dimensional, then...
Equalities for orthogonal projectors and their operations
A complex square matrix A is called an orthogonal projector if A 2 = A = A*, where A* denotes the conjugate transpose of A. In this paper, we give a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. We first collect some well-known rank formulas for orthogonal projectors and their operations, and then establish various new rank formulas for matrix expressions composed by orthogonal projectors. As applications, we...
Erratum to "Algebraic and topological properties of some sets in ℓ₁" (Colloq. Math. 129 (2012), 75-85)
Essential sign change numbers of full sign pattern matrices
A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced for full sign...
Even and odd tournament matrices with minimum rank over finite fields.
Existence and construction of two-dimensional invariant subspaces for pairs of rotations
By a rotation in a Euclidean space V of even dimension we mean an orthogonal linear operator on V which is an orthogonal direct sum of rotations in 2-dimensional linear subspaces of V by a common angle α ∈ [0,π]. We present a criterion for the existence of a 2-dimensional subspace of V which is invariant under a given pair of rotations, in terms of the vanishing of a determinant associated with that pair. This criterion is constructive, whenever it is satisfied. It is also used to prove that every...
Existence theorems for commutative diagrams.
Extension of -dimensional Euclidean vector space over to pseudo-fuzzy vector space over .
Extreme preservers of maximal column rank inequalities of matrix sums over semirings
We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings.
Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation.