Linear Algebra Done Right · Problem 6C.23

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · pseudoinverse

Problem

Suppose

V

and

W

are finite-dimensional and

T \in \mathcal{L}(V, W)

. Prove that

(T^\dagger)^\dagger = T.

The equation above is analogous to the equation

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

that holds if

T

is invertible.