Let each of the sets of vectors {u1,u2,.....,um} and {w1,w2,.......,wm} form an orthonormal basis for a subspace W Rn . If the m x m matrix A is defined by the condition that

Prove that ATA = Im, the m x m identity matrix.
Hint: w=uA, where w is the n x m matrix whose jth column is wj and similarly for the
n x m matrix u.