Linear Algebra and Its Applications · Problem 3.3.11

Orthogonality — Gilbert Strang

Mathematics · projection-orthogonal-complement

Problem

Suppose

P

is the projection matrix onto the subspace

\mathbf{S}

and

Q

is the projection onto the orthogonal complement

\mathbf{S}^\perp

. What are

P + Q

and

PQ

? Show that

P - Q

is its own inverse.