16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.4.2

Inner Product Spaces

Mathematics — Linear Algebra · unitary-operators

Problem

Let VV be the space of complex n×nn \times n matrices with inner product (A∣B)=tr⁡(AB∗)(A|B) = \operatorname{tr}(AB^*). For each MM in VV, let TMT_M be the linear operator defined by TM(A)=MAT_M(A) = MA. Show that TMT_M is unitary if and only if MM is a unitary matrix.

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