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singular_values_of_a_matrix [2014/03/21 11:11] |
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| + | ===== Singular values of a matrix ===== | ||
| + | ==== Set ==== | ||
| + | | @#55CCEE: context | @#55CCEE: $ A \in \mathrm{SquareMatrix}(n,\mathbb C) $ | | ||
| + | | @#FFBB00: definiendum | @#FFBB00: $ \sqrt{\lambda} \in \mathrm{SingularVal}(A) $ | | ||
| + | |||
| + | | @#55EE55: postulate | @#55EE55: $ \lambda \in \mathrm{EigenVal}(A^*A) $ | | ||
| + | |||
| + | ==== Discussion ==== | ||
| + | Note that $A^*A$ is always Hermitian positive semi-definite matrix. | ||
| + | |||
| + | Singular values make sense for more general operators too. | ||
| + | === Reference === | ||
| + | Wikipedia: [[http://en.wikipedia.org/wiki/Singular_value|Singular value]], [[http://en.wikipedia.org/wiki/Matrix_norm|Matrix norm]] | ||
| + | ==== Parents ==== | ||
| + | === Context === | ||
| + | [[Matrix eigenvalue]] | ||
