Please help q954 Find a reduced singular value decomposition

Please help (q9.5.4)

Find a reduced singular value decomposition of A. A = [18 12 0 0 12 0] Enter each matrix below enter as value only.

Solution:

A^transpose_*A= 468 216

216 144

The eigenvalues (in order of decreasing magnitude) are 1 = 576 and 2 = 36, and the corresponding eigenvectors

v1 = 0.894 v2 = -0.447

0.447 0.894

Therefore, V^Transpose = 0.894 0.447

-0.447 0.894

1 = 1 = 576 = 24 and 2 = 2 = 36 = 6

Therefore: = 24 0 but since we have to find 1*1 value of . Taking 6 common. = [4]

0 6

First column of U: u1 = (1/1)*A*v1

Similarily, Second column u2 = (1/2)*A*v2

Therefore: U = 0.894 0.447

0 0

0.447 -0.894

But as we had taken a scalar of 6 common from , So multiplying it with either U or V^Transpose

Let us multiply the scalar 6 with U.

Thus final U becomes = 5.364 2.682

0 0

2.682 -5.364