HIGHER RANK NUMERICAL RANGES OF NORMAL MATRICES

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/51196

Title:	HIGHER RANK NUMERICAL RANGES OF NORMAL MATRICES
Authors:	Gau,HL;Li,CK;Poon,YT;Sze,NS
Contributors:	數學系
Keywords:	ERROR-CORRECTING CODES
Date:	2011
Issue Date:	2012-03-27 18:24:38 (UTC+8)
Publisher:	國立中央大學
Abstract:	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 is an element of M(n) has eigenvalues a(1), ..., a(n), then its higher rank numerical range Lambda(k)(A) is the intersection of convex polygons with vertices a(j1), ..., a(jn-k+1), where 1 <= j(1) < ... < j(n-k+1) <= n. In this paper, it is shown that the higher rank numerical range of a normal matrix with m distinct eigenvalues can be written as the intersection of no more than max{m, 4} closed half planes. In addition, given a convex polygon P, a construction is given for a normal matrix A is an element of M(n) with minimum n such that Lambda(k)(A) = P. In particular, if P has p vertices, with p >= 3, there is a normal matrix A is an element of M(n) with n <= max {p + k - 1, 2k + 2} such that Lambda(k)(A) = P.
Relation:	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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