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pro vyhledávání: '"15a60"'
The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correction. We will discuss some of the real algebraic and convex geometry of
Externí odkaz:
http://arxiv.org/abs/2410.21625
Autor:
Christensen, Erik
The Schur product of two complex m x n matrices is their entry wise product. We show that an extremal element X in the convex set of m x n complex matrices of Schur multiplier norm at most 1 satisfies the inequality rank(X) =< (m +n)^(1/2) . For posi
Externí odkaz:
http://arxiv.org/abs/2410.20112
We investigate when the algebraic numerical range is a $C$-spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix algebras and
Externí odkaz:
http://arxiv.org/abs/2410.10678
This paper considers the problem of computing the operator norm of a linear map between finite dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions. We propose a stochastic method
Externí odkaz:
http://arxiv.org/abs/2410.08297
Autor:
Balan, Radu, Jiang, Fushuai
A problem by Feichtinger, Heil, and Larson asks whether a positive-definite integral operator with $M_1$ kernel admits a symmetric rank-one decomposition which is strongly square-summable with respect to the $M_1$ norm. In conjunction with a concurre
Externí odkaz:
http://arxiv.org/abs/2409.20372
Autor:
Herrera, David
Resolving a conjecture of von Neumann, Ogata's theorem in arXiv:1111.5933 showed the highly nontrivial result that arbitrarily many matrices corresponding to macroscopic observables with $N$ sites and a fixed site dimension $d$ are asymptotically nea
Externí odkaz:
http://arxiv.org/abs/2409.14636
The Crouzeix ratio $\psi(A)$ of an $N\times N$ complex matrix $A$ is the supremum of $\|p(A)\|$ taken over all polynomials $p$ such that $|p|\le 1$ on the numerical range of $A$. It is known that $\psi(A)\le 1+\sqrt{2}$, and it is conjectured that $\
Externí odkaz:
http://arxiv.org/abs/2409.14127
Autor:
Li, Chi-Kwong, Wang, Kuo-Zhong
We refine a recent result of Drury concerning the optimal ratio between the norm and numerical radius of a bounded linear operator $T$ with numerical range lying in a sector of a circular disk. In particular, characterization is given to the operator
Externí odkaz:
http://arxiv.org/abs/2409.18135
Autor:
Frankel, Elsa, Urschel, John
We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for fully resolving a conjecture of Harwitz and Sloane, commonly referred to
Externí odkaz:
http://arxiv.org/abs/2409.04354
We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterization of the solutions is obtained in the case when the underlying graph i
Externí odkaz:
http://arxiv.org/abs/2409.04146