16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.6.9

Elementary Canonical Forms

Mathematics — Linear Algebra · identity-plus-projection-invertible

Problem

Let

V

be a real vector space and

E

an idempotent linear operator on

V

, i.e., a projection. Prove that

(I + E)

is invertible. Find

(I + E)^{-1}