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Explicit solutions of infinite linear systems associated with group inverse endomorphisms

Fernando Pablos Romo (2022)

Czechoslovak Mathematical Journal

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.

From geometry to invertibility preservers

Hans Havlicek, Peter Šemrl (2006)

Studia Mathematica

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

Irina Perfilieva (2007)

Acta Mathematica Universitatis Ostraviensis

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 F -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.

G-tridiagonal majorization on 𝐌 n , m

Ahmad Mohammadhasani, Yamin Sayyari, Mahdi Sabzvari (2021)

Communications in Mathematics

For X , Y ∈ 𝐌 n , m , it is said that X is g-tridiagonal majorized by Y (and it is denoted by X ≺ g t Y ) if there exists a tridiagonal g-doubly stochastic matrix A such that X = A Y . In this paper, the linear preservers and strong linear preservers of ≺ g t are characterized on 𝐌 n , m .

Immanant Conversion on Symmetric Matrices

M. Purificação Coelho, M. Antónia Duffner, Alexander E. Guterman (2014)

Special 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

Seok-Zun Song, Kyung-Tae Kang, Young Bae Jun (2006)

Czechoslovak Mathematical Journal

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

Hiroyuki Ishibashi (2006)

Czechoslovak Mathematical Journal

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.

Stephen Pierce, William Watkins (1979)

Journal für die reine und angewandte Mathematik

Kronecker modules and reductions of a pair of bilinear forms

Giovanni Falcone, M. Alessandra Vaccaro (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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.

Linear extensions of relations between vector spaces

Árpád Száz (2003)

Commentationes Mathematicae Universitatis Carolinae

Let X and Y be vector spaces over the same field K . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λ F ( x ) ⊂ F ( λ x ) and F ( x ) + F ( y ) ⊂ F ( x + y ) for all λ ∈ K ∖ { 0 } and x , y ∈ X . After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X into Y can be extended to a linear relation F of X into Y if and only if there exists a linear subspace Z of Y such that Φ ( e ) ∈ Y | Z for all e ∈ E . Moreover, if E generates...

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