Exercise 4.2.21

Answers

{(A {(A^{T} A)}^{- 1} A^{T})}^{2} = A {(A^{T} A)}^{- 1} (A^{T} A) {(A^{T} A)}^{- 1} A^{T} = A {(A^{T} A)}^{- 1} A^{T} .

So $P^{2} = P$ . $P b$ is in the column space (where $P$ projects). Then its projection $P (P b)$ is also $P b$ .

mathchakra

2023-09-14 07:38