Higher rank numerical ranges of normal matrices

Hwa Long Gau, Chi Kwong Li, Yiu Tung Poon, Nung Sing Sze

研究成果: 雜誌貢獻期刊論文同行評審

15 引文 斯高帕斯(Scopus)

摘要

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 ε Mn has eigenvalues a1, ⋯ , a n, then its higher rank numerical range Γκ(A) is the intersection of convex polygons with vertices aj1 , ⋯ , ajn-k+1, where 1 ≤ j1 < ⋯ ≤ 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 ε Mn with minimum n such that Δκ(A) = P. In particular, if P has p vertices, with p ≥ 3, there is a normal matrix A ε Mn with n ≤ max {p + k -1, 2k + 2} such that Γκ(A) = P.

原文???core.languages.en_GB???
頁(從 - 到)23-43
頁數21
期刊SIAM Journal on Matrix Analysis and Applications
32
發行號1
DOIs
出版狀態已出版 - 2011

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