16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.2.10

Inner Product Spaces

Mathematics — Linear Algebra · orthogonal-complement

Problem

Let

V

be the vector space of all

n \times n

matrices over

C

, with the inner product

(A|B) = \operatorname{tr}(AB^*)

. Find the orthogonal complement of the subspace of diagonal matrices.