### 15.3.7 Singular values (HP compatible)

The singular values of a matrix A are the positive square roots of the eigenvalues of A AT. So, if A is symmetric, the singular values are the absolute values of the eigenvalues of A. The SVL or svl command finds the singular values of a matrix.

- SVL takes A, a matrix.
- SVL(A) returns a list of the singular values of A.

#### Examples

SVL([[1,2],[3,4]])

| ⎡ ⎣ | 0.365966190626,5.46498570422 | ⎤ ⎦

evalf(sqrt(eigenvals([[1,2],[3,4]]*transpose([[1,2],[3,4]]))))

5.46498570422,0.365966190626 |  |  |  |  |  |  |  |  |  |

svl([[1,4],[4,1]])

| ⎡ ⎣ | 5.0,3.0 | ⎤ ⎦

abs(eigenvals([[1,4],[4,1]]))

5,3 |  |  |  |  |  |  |  |  |  |