16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.3.5

Inner Product Spaces

Mathematics — Linear Algebra · adjoint-operators

Problem

Let

V

be a finite-dimensional inner product space and

T

a linear operator on

V

. If

T

is invertible, show that

T^*

is invertible and

(T^*)^{-1} = (T^{-1})^*