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. © 2006 Elsevier Inc. All rights reserved.
Choi, M. D., Kribs, D. W., & Zyczkowski, K. (2006). Higher-rank numerical ranges and compression problems. Linear Algebra and Its Applications, 418(2–3), 828–839. https://doi.org/10.1016/j.laa.2006.03.019