Matrices hermitian for an absolute norm
Hans Schneider, Robert E. L. Turner · Linear and Multilinear Algebra · 1973
Letv be a (standardized) absolute norm onC:n . A matrix Hin Cnn is called norm-Hermitian if the numerical range V(H) determined by vis real. Let be the set of all norm-Hermitians in Cnn .We determine an equivalence relation ∼ on {1,…,n) with the following property: Let H ε Cnn Then if and only if His Hermitian and . Let is a subalgebra of Cnn and, for V(A) equals the Euclidean numerical range and hence is convex. Let be the group of isometries forv,and let Then is a normal subgroup of and where is a group of permutation matrices.