The generalized spectral radius, numerical radius and spectral norm
Chi-Kwong Li, Tin-Yau Tam, Nam‐Kiu Tsing · Linear and Multilinear Algebra · 1984
Given n×n complex matrices A, C with eigenvalues αj, γj, 1 ⩾ j ⩾ n, respectively, we have the relation where and respectively are the generalized spectral radius, generalized numerical radius and generalized spectral norm of A with respect to C. For C = diag(1,0,…,0), it reduces to the classical relation In this note, we investigate matrices for which . The norm properties of are also studied.