Die Reduction linearer homogener Substitutionen von endlicher Periode auf ihre kanonische Form.
Direct summands of systems of continuous linear transformations [Book]
Endomorphism rings of valued vector spaces
Explicit solutions of infinite linear systems associated with group inverse endomorphisms
The aim of this note is to offer an algorithm for studying solutions of infinite linear systems associated with group inverse endomorphisms. As particular results, we provide different properties of the group inverse and we characterize EP endomorphisms of arbitrary vector spaces from the coincidence of the group inverse and the Moore-Penrose inverse.
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.
From geometry to invertibility preservers
We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.
Fuzzy transforms in image compression and fusion
An overview of direct and inverse fuzzy transforms of three types is given and applications to data processing are considered. The construction and some important properties of fuzzy transforms are presented on the theoretical level. Three applications of -transform to data processing have been chosen: compressional and reconstruction of data, removing noise and data fusion. All of them successively exploit the filtering property of the inverse fuzzy transform.
General preservers of quasi-commutativity on Hermitian matrices.
Geometric aspects of linear transformations of the plane.
G-tridiagonal majorization on
For , it is said that is g-tridiagonal majorized by (and it is denoted by ) if there exists a tridiagonal g-doubly stochastic matrix such that . In this paper, the linear preservers and strong linear preservers of are characterized on .
Idempotence-preserving maps between matrix spaces over fields of characteristic 2.
Immanant Conversion on Symmetric Matrices
Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).
Invertible commutativity preservers of matrices over max algebra
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra.
Involutions and semiinvolutions
We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.
Isometries of E2.
Iteration einer n-Ecksabbildung.
Kronecker modules and reductions of a pair of bilinear forms
We give a short overview on the subject of canonical reduction of a pair of bilinear forms, each being symmetric or alternating, making use of the classification of pairs of linear mappings between vector spaces given by J. Dieudonné.
Left eigenvalues of symplectic matrices.
Linear extensions of relations between vector spaces
Let and be vector spaces over the same field . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation of into is called linear if and for all and . After improving and supplementing some former results on linear relations, we show that a relation of a linearly independent subset of into can be extended to a linear relation of into if and only if there exists a linear subspace of such that for all . Moreover, if generates...
Linear fractional transformations and companion matrices