Higher-rank Numerical Ranges and Kippenhahn Polynomials

Hwa-Long Gau, Pei Yuan Wu

We prove that two n-by-n matrices A and B have their rank-k numerical ranges ${\Lambda }_k(A)$ and ${\Lambda }_k(B)$ equal to each other for all k, $1\le k\le \lfloor n/2\rfloor +1$, if and only if t…