Linear Algebra Done Right · Problem 7B.10

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · spectral-theorem

Problem

Suppose

V

is a complex inner product space. Prove that every normal operator on

V

has a square root. An operator

S \in \mathcal{L}(V)

is called a square root of

T \in \mathcal{L}(V)

S^2 = T

. We will discuss more about square roots of operators in Sections 7C and 8C.