Compute the singular values of the following matrices X1 1

Compute the singular values of the following matrices. X_1 = [-1 1 0 0 1 1] X_2 = [-1 1 0 1 1 0 1 -1].

Solution

2

(i)

Singular values:
1.7321 1.0000

Matrix U:
-0.7071 -0.7071
-0.7071 0.7071

Matrix V:
0.4082 0.7071 -0.5774
-0.8165 0.0000 -0.5774
-0.4082 0.7071 0.5774

2

(ii)

Singular values:
2.2361 1.0000

Matrix U:
-0.6325 -0.0000 0.4885 0.6012
-0.3162 -0.7071 -0.6109 0.1637
0.3162 -0.7071 0.6109 -0.1637
0.6325 0.0000 -0.1224 0.7649

Matrix V:
0.7071 -0.7071
-0.7071 -0.7071