Preservers of matrix pairs with a fixed inner product value
Chi-Kwong Li, Lucijan Plevnik, Peter Šemrl · Operators and Matrices · 2012
Let V be the set of n n hermitian matrices, the set of n n symmetric matrices, the set of all effects, or the set of all projections of rank one. Let c be a real number. We characterize bijective maps : V V satisfying tr (AB) = c tr ( (A) (B)) = c with some additional restrictions on c , depending on the underlying set of matrices.