Convexity of the joint numerical range: topological and differential geometric viewpoints
نویسندگان
چکیده
منابع مشابه
Convexity of the Joint Numerical Range: Topological and Differential Geometric Viewpoints
The purpose of this paper is to show that the joint numerical range of am-tuple of n×n hermitian matrices is convex whenever the largest eigenvalue of an associated family of hermitian matrices parameterized by the (m − 1)-dimensional sphere has constant multiplicity and, as a more technical condition, the union over the sphere of the largest eigenvalue eigenspaces does not fill the full n-dime...
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برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولThe Joint Essential Numerical Range of operators: Convexity and Related Results
LetW (A) andWe(A) be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A1, . . . , Am) acting on an infinite dimensional Hilbert space, respectively. In this paper, it is shown that We(A) is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ {1, . . . ,m}, We(A) can be obtained as the intersection ...
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The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2003.06.011