Page 106 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

94 Chapter 3

and the Diagonal matrix ^ obtained as the positive square root of the
T
T
elements of the eigen values computed for the matrix AA (or) A A

(i.e.) The Eigen values are same for both the matrices.
3.1 Example

The matrix A is applied to SVD as follows.
A =
1 2 3
4 5 6

U =
-0.3863 -0.9224
-0.9224 0.3863

V =
-0.4287 0.8060 0.4082
-0.5663 0.1124 -0.8165
-0.7039 -0.5812 0.4082

^ =
0
9.5080 0

0
0.7729 0

U*^*V' =

1.0000 2.0000 3.0000
4.0000 5.0000 6.0000
Eigen values of (A'*A) = E 1

-0.0000
0.5973
90.4027

Eigen values of (A*A’) = E 2

0.5973
90.4027

Note that the diagonal elements of the ^ is obtained as the square root of
E 1 or E 2 .