16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 9.5.2

Operators on Inner Product Spaces

Mathematics — Linear Algebra · matrix-exponential-unitary

Problem

Let

A

be an

n \times n

matrix with complex entries such that

A^* = -A

, and let

B = e^A

. Show that (a)

\det B = e^{\operatorname{tr} A}

; (b)

B^* = e^{-A}

; (c)

B

is unitary.