Singular values (HP compatible)

15.3.7 Singular values (HP compatible)

The singular values of a matrix A are the positive square roots of the eigenvalues of A A^T. 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

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⎦

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

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⎦

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

5,3