A generalization of spectral radius, numerical radius, and spectral norm
The author defines three quantities, \(\rho\) (A), r(A), and \(\| A\|\), as scalar functions of a matrix A. These are \(\ell_ p\) norms of tuples formed respectively from the eigenvalues of A, the diagonal of a unitary similarity of A (that is, \(UAU^*)\), and the diagonal of a matrix unitarily equivalent to A (that is, UAV), where U, V are to be unitary. In the second and third possibilities, r and \(\| \cdot \|\) are the maximum of the specified \(\ell_ p\) norms as U and V vary over all unitary matrices. The author studies those matrices A for which equalities exist among \(\rho\) (A), r(A), and \(\| A\|\). Furthermore, the norm properties of r(A) and \(\| A\|\) are investigated.
scientific article; zbMATH DE number 4012825
scientific article