Higher Rank Numerical Ranges of Normal Matrices

  • Authors:
  • Hwa-Long Gau;Chi-Kwong Li;Yiu-Tung Poon;Nung-Sing Sze

  • Affiliations:
  • hlgau@math.ncu.edu.tw;ckli@math.wm.edu;ytpoon@iastate.edu;raymond.sze@inet.polyu.edu.hk

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 2011

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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 $A\in M_n$ has eigenvalues $a_1,\dots,a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1},\dots,a_{j_{n-k+1}}$, where $1\leq j_1