6.49.7  Singular values (HP compatible): SVL svl

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 is a synonym for SVL.

• SVL takes one argument:
  A, a matrix.
• SVL(A) returns a list of the singular values of A.

Examples.

• Input:
  SVL([[1,2],[3,4]])
  or:
  svl([[1,2],[3,4]])
  Output:

  ⎡ ⎣

  0.365966190626,5.46498570422

  ⎤ ⎦

• Input:
  evalf(sqrt(eigenvals([[1,2],[3,4]]*transpose([[1,2],[3,4]]))))
  Output:

  5.46498570422,0.365966190626

• Input:
  SVL([[1,4],[4,1]])
  or:
  svl([[1,4],[4,1]])
  Output:

  ⎡ ⎣

  5.0,3.0

  ⎤ ⎦

  Input:
  abs(eigenvals([[1,4],[4,1]]))
  Output:

  5,3