نتایج جستجو برای: joint higher rank numerical range

تعداد نتایج: 2065797  

2007
YUAN WU

For any n-by-n complex matrix A and any k, 1 ≤ k ≤ n, let Λk(A) = {λ ∈ C : X∗AX = λIk for some n-by-k X satisfying X∗X = Ik} be its rank-k numerical range. It is shown that if A is an n-by-n contraction, then Λk(A) = ∩{Λk(U) : U is an (n + dA)-by-(n + dA) unitary dilation of A}, where dA = rank (In − A∗A). This extends and refines previous results of Choi and Li on constrained unitary dilations...

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.

2006
MAN-DUEN CHOI DAVID W. KRIBS

We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and give a complete description in the Hermitian case. We also consider associated projection compression problems.

Journal: :SIAM J. Matrix Analysis Applications 2011
Hwa-Long Gau Chi-Kwong Li Yiu-Tung Poon Nung-Sing Sze

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix A ∈ Mn has eigenvalues a1, . . . , an, then its higher rank numerical range Λk(A) is the intersection of convex polygons with vertices aj1 , . . . , ajn−k+1 , where 1 ≤ j1 < · · · < jn−k+1 ≤ n. In this paper, it is shown that ...

Journal: :AL-Rafidain Journal of Computer Sciences and Mathematics 2009

Journal: :Linear Algebra and its Applications 2015

2015
MAO-TING CHIEN CHI-KWONG LI MING-CHENG TSAI KUO-ZHONG WANG

We show that a bounded linear operator A ∈ B(H) is a multiple of a unitary operator if and only if AZ and ZA always have the same numerical radius or the same numerical range for all (rank one) Z ∈ B(H). More generally, for any bounded linear operators A,B ∈ B(H), we show that AZ and ZB always have the same numerical radius (resp., the same numerical range) for all (rank one) Z ∈ B(H) if and on...

Journal: :Applied Mathematics Letters 2001

Journal: :Studia Mathematica 2022

It is shown that for $n \le 3$ the joint numerical range of a family commuting $n\times n$ complex matrices always convex; \ge 4$ there are two whose not convex.

Journal: :Linear Algebra and its Applications 2010

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