Using this decomposition, construct the orthogonal projection (P) on the column space of (A) in terms of the matrices in the SVD (or their elements, such as columns).

a) Find the eigenvalues of the matrix
b) Express (P) as (A(AᵗA)⁻¹Aᵗ)
c) Calculate the singular value decomposition of (A)
d) Determine the rank of the matrix