Set
A = round(10 * rand(10, 5)) and s = svd(A)
(a) Set
[U, D, V] = svd(A); D(5,5)=0; B = U*D*Vʹ
The matrix B should be the closest matrix of rank 4 to A (where distance is measured in terms of the Frobenius norm). Compute ||A||2 and ||6||2. How do these values compare? Compute and compare the Frobenius norms of the two matrices. Compute also ||A - B||F and compare the result to s(5). Set r = norm(s(l : 4)) and compare the result to ||B||F.
(b) Use MATLAB to construct a matrix C that is the closest matrix of rank 3 to A with respect to the Frobenius norm. Compute ||C||2 and ||C||F. How do these values compare with the computed values for ||A||2 and ||A||F? Set
p = norm(s(l : 3)) and q = norm(s(4 : 5))
Compute ||C||F and ||A - C||F and compare your results to p and q.