Zobrazeno 1 - 10
of 52
pro vyhledávání: '"15a10"'
For given real or complex $m \times n$ data matrices $X$, $Y$, we investigate when there is a matrix $A$ such that $AX = Y$, and $A$ is invertible, Hermitian, positive (semi)definite, unitary, an orthogonal projection, a reflection, complex symmetric
Externí odkaz:
http://arxiv.org/abs/2408.10036
Autor:
Vigneaux, Juan Pablo
We use Cramer's formula for the inverse of a matrix and a combinatorial expression for the determinant in terms of paths of an associated digraph (which can be traced back to Coates) to give a combinatorial interpretation of M\"obius inversion whenev
Externí odkaz:
http://arxiv.org/abs/2407.14647
Autor:
Kędzierski, Oskar
We generalize the Wedderburn rank reduction formula by replacing the inverse with the Moore--Penrose pseudoinverse. In particular, this allows one to remove the non--singularity of a certain matrix from assumptions. The results implies in a straightf
Externí odkaz:
http://arxiv.org/abs/2406.03992
Autor:
Leonov, A. S.
We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it possible
Externí odkaz:
http://arxiv.org/abs/2405.04399
Autor:
Comănescu, Dan
We prove that the following statements are equivalent: a linear matrix equation with parameters forming a commuting set of diagonalizable matrices is consistent, a certain matrix constructed with the Drazin inverse is a solution of this matrix equati
Externí odkaz:
http://arxiv.org/abs/2406.09429
Autor:
Ferreyra, D. E., Mosic, D.
Recently, Malik and Ferreyra introduced the $m$-weak core inverse for complex square matrices which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. The main aim of this paper is to extend the concept of $m$-weak core
Externí odkaz:
http://arxiv.org/abs/2403.14196
Large-scale linear systems, $Ax=b$, frequently arise in practice and demand effective iterative solvers. Often, these systems are noisy due to operational errors or faulty data-collection processes. In the past decade, the randomized Kaczmarz (RK) al
Externí odkaz:
http://arxiv.org/abs/2308.16904
Autor:
Green, Nathaniel K., Kim, Edward D.
We prove that the coefficient of $t^2$ in $\mathsf{trace}((A+tB)^6)$ is a sum of squares in the entries of the symmetric matrices $A$ and $B$.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2307.06311
Autor:
Karpowicz, Michał P.
This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the column space and one for the row space of a matrix, and how to calcula
Externí odkaz:
http://arxiv.org/abs/2304.12451
Autor:
Chen, Stephanie, Vigneaux, Juan Pablo
Publikováno v:
Bull. Belg. Math. Soc. Simon Stevin 30(3): 341-353 (November 2023)
The magnitude of finite categories is a generalization of the Euler characteristic. It is defined using the coarse incidence algebra of rational-valued functions on the given finite category, and a distinguished element in this algebra: the Dirichlet
Externí odkaz:
http://arxiv.org/abs/2303.12176