Kunze Linear Algebra · Problem 8.2.10

Inner Product Spaces

Mathematics — Methods · orthogonal-complement-matrices

Problem

Let VV be the vector space of all n×nn \times n matrices over CC, with the inner product (A∣B)=tr⁡(AB∗)(A|B) = \operatorname{tr}(AB^*). Find the orthogonal complement of the subspace of diagonal matrices.

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