16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.3.10

Inner Product Spaces

Mathematics — Linear Algebra · adjoint-operators-matrices

Problem

Let VV be the space of n×nn \times n matrices over the complex numbers, with the inner product (A,B)=tr⁡(AB∗)(A, B) = \operatorname{tr}(AB^*). Let PP be a fixed invertible matrix in VV, and let TPT_P be the linear operator on VV defined by TP(A)=P−1APT_P(A) = P^{-1}AP. Find the adjoint of TPT_P.

Related theory

Browse the problem library