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singular_values_of_a_matrix [2014/03/21 11:11] (current)
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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]]
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