Results 11 to 20 of about 641 (72)
Linear maps preserving rank 2 on the space of alternate matrices and their applications
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 63, Page 3409-3417, 2004., 2004 Denote by đŠn(F) the linear space of all n Ă n alternate matrices over a field F. We first characterize all linear bijective maps on đŠn(F)(n â„ 4) preserving rank 2 when F is any field, and thereby the characterization of all linear bijective maps on đŠn(F) preserving the maxârank is done when F is any field except for {0, 1} .
Chongguang Cao, Xiaomin Tang
wiley +1 more source
Rank Function Equations and their solution sets [PDF]
, 2013 We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.Comment: 8 pages, all
Pokora, Piotr
core +2 more sources
Basic Operations on Supertropical Quadratic Forms
Documenta Mathematica, 2017 In the case that a module V over a (commutative) supertropical semiring R is free, the R-module Quad(V ) of all quadratic forms on V is almost never a free module.
Z. Izhakian, Manfred Knebusch
semanticscholar +1 more source
A hierarchy in the family of real surjective functions
Open Mathematics, 2017 This expository paper focuses on the study of extreme surjective functions in ââ. We present several different types of extreme surjectivity by providing examples and crucial properties.
Fenoy-Muñoz Mar +3 more
doaj +1 more source
On sequences not enjoying Schurâs property
Open Mathematics, 2017 Here we proved the existence of a closed vector space of sequences - any nonzero element of which does not comply with Schurâs property, that is, it is weakly convergent but not norm convergent. This allows us to find similar algebraic structures in some
JimĂ©nez-RodrĂguez Pablo
doaj +1 more source
Closed-form formula for a classical system of matrix equations
Arab Journal of Basic and Applied Sciences, 2022 Keeping in view the latest development of anti-Hermitian matrix in mind, we construct some closed form formula for a classical system of matrix equations having anti-Hermitian nature in this paper.
Abdur Rehman +4 more
doaj +1 more source
Monotone transformations on B(H) with respect to the left-star and the right-star partial order
, 2014 Let H be an infinite dimensional complex Hilbert space, and let B(H) be the set of all bounded linear operators on H . In the paper equivalent definitions for the left-star and the right-star partial orders on B(H) are given and bijective additive maps ...
G. Dolinar, A. Guterman, J. Marovt
semanticscholar +1 more source
Rank relations between a {0, 1}-matrix and its complement
Open Mathematics, 2018 Let A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J â A, where J is the matrix with each entry being 1.
Ma Chao, Zhong Jin
doaj +1 more source
Lineability, spaceability, and additivity cardinals for Darboux-like functions [PDF]
, 2013 We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of M.
Aron +32 more
core +2 more sources
The maximal and minimal ranks of matrix expression with applications
Journal of Inequalities and Applications, 2012 We give in this article the maximal and minimal ranks of the matrix expression A-B1V1C1-B2V2C2-B3V3C3-B4V4C4 with respect to V1, V2, V3, and V4. As applications, we derive the extremal ranks of the generalized Schur complement A - BM(1)C - DN(1)G and the
Zhiping Xiong +2 more
semanticscholar +2 more sources