I have a 3x2 matrix A = {{1,-1},{2,-1},{3,1}}. I need to find the orthogonal projection matrix P onto the range of A.
I know that the orthogonal projection is the outer-product / inner-product, that is to say A*transpose(A) / transpose(A)*A.
I am stuck when I try to find the inner-product, as I thought that it is supposed to be scalar (as is the case when A is a vector).
Could it be that I should split the matrix A into 2 vectors, and add the projections?
Ok, I solved it.
The first formula only works when A is a single vector.
If I rearrange the terms such that P = A * (transpose(A)*A)^-1 * transpose(A), then it allows me to use a basis with more than one vector.