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SingularValues

SingularValues[m] gives the singular value decomposition for a numerical matrix m.

• The result of SingularValues[m] is a list {u, w, v , where w is the list of singular values and m can be written as Conjugate[Transpose[u]] . DiagonalMatrix[w] . v.
u and v are row orthonormal matrices, which can be considered as lists of orthonormal vectors.
• The ratio of the largest to smallest singular value gives the  condition number of m.

Examples

Using InstantCalculators

Here is the InstantCalculator for the SingularValues function. Enter the parameters for your calculation and click Calculate to see the result.

Entering Commands Directly

You can paste a template for this command via the Text Input button on the SingularValues Function Controller.

This is the singular value decomposition of a non-singular  Cross  inexact matrix.

This checks the result using the shorthand form of Dot.

This is the singular value decomposition of a singular matrix. Only one singular value is given.



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