Results 11 to 20 of about 594 (68)

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

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, Ivan I. Kyrchei, Israr Ali Khan, Muhammad Nasir, Imran Ali   +4 more
doaj   +1 more source

Lineability of non-differentiable Pettis primitives [PDF]

, 2014
Let X be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an X-valued Pettis integrable function on [0; 1] whose primitive is nowhere weakly differentiable.
Bongiorno, B., Darju, U. B., Di Piazza, L.   +2 more
core   +1 more source

Limits of Sequences of Feebly-Type Continuous Functions

Annales Mathematicae Silesianae, 2020
We consider the following families of real-valued functions defined on 𝕉2: feebly continuous functions (FC), very feebly continuous functions (VFC), and two-feebly continuous functions (TFC). It is known that the inclusions FC ⊂ VFC ⊂ TFC are proper.
Balcerzak Marek, Natkaniec Tomasz, Terepeta Małgorzata   +2 more
doaj   +1 more source

On sequences not enjoying Schur’s 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 Schur’s property, that is, it is weakly convergent but not norm convergent. This allows us to find similar algebraic structures in some
Jiménez-Rodríguez Pablo
doaj   +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 − A, where J is the matrix with each entry being 1.
Ma Chao, Zhong Jin
doaj   +1 more source

A completely entangled subspace of maximal dimension

, 2004
A completely entangled subspace of a tensor product of Hilbert spaces is a subspace with no non-trivial product vector. K. R. Parthasarathy determined the maximum dimension possible for such a subspace.
Bhat, B. V. Rajarama
core   +1 more source

From primitive spaces of bounded rank matrices to a generalized Gerstenhaber theorem

, 2013
A recent generalization of Gerstenhaber's theorem on spaces of nilpotent matrices is derived, under mild conditions on the cardinality of the underlying field, from Atkinson's structure theorem on primitive spaces of bounded rank matrices.Comment: 10 ...
Pazzis, Clément de Seguins
core   +2 more sources

Matrix rank and inertia formulas in the analysis of general linear models

Open Mathematics, 2017
Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and ...
Tian Yongge
doaj   +1 more source

Generalized Chebyshev Polynomials

Discussiones Mathematicae - General Algebra and Applications, 2018
Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind Tn and Un. We show that they are in a ℚ-vectorial subspace En(x) of ℚ[x] of dimension n.
Abchiche Mourad, Belbachir Hacéne
doaj   +1 more source