Show that if {v1,..., vk} is an orthonormal basis of a subspace E of C^n, then the orthogonal projection matrix P_E:C^n --> C^n is P =the sum as i goes from 1 to k of (vi)(vi bar)^t.
An orthonormal basis is if <vi, vj> = 0 when i does not equal j and if the length of vi is 1. vi bar is the complex conjugate of vi and (vi bar)^t is the transpose of that.
Would I show this by showing that the projection of v onto itself is SUM(<vi, vi> vi)?