Singular values and numerical radii
Marvin D. Marcus, Markus Sandy · Linear and Multilinear Algebra · 1985
The purpose of this paper is to prove the following result relating the singular values and the numerical radius of the matrix: For any n-square.complex matrix A with singular values αl ⩾ [cddot] ⩾ αn ⩾ 0 and numerical radius r(A) with equality if and only if A r (A) is unitarily similar to the direct sum of a diagonal unitary matrix and unit multiples of 2 × 2 matrices of the form where