Editing Hermitian matrix (section)

=== Singular values ===
The singular values of <math>A</math> are the absolute values of its eigenvalues:

Since <math>A</math> has an eigendecomposition <math>A=U\Lambda U^H</math>, where <math>U</math> is a [[unitary matrix]] (its columns are orthonormal vectors; [[Hermitian matrix#Eigendecomposition|see above]]), a [[singular value decomposition]] of <math>A</math> is <math>A=U|\Lambda|\text{sgn}(\Lambda)U^H</math>, where <math>|\Lambda|</math> and <math>\text{sgn}(\Lambda)</math> are diagonal matrices containing the absolute values <math>|\lambda|</math> and signs <math>\text{sgn}(\lambda)</math> of <math>A</math>'s eigenvalues, respectively. <math>\sgn(\Lambda)U^H</math> is unitary, since the columns of <math>U^H</math> are only getting multiplied by <math>\pm 1</math>. <math>|\Lambda|</math> contains the singular values of <math>A</math>, namely, the absolute values of its eigenvalues.<ref>{{Cite book |last1=Trefethan |first1=Lloyd N. |url=http://worldcat.org/oclc/1348374386 |title=Numerical linear algebra |last2=Bau, III |first2=David |publisher=[[SIAM]] |year=1997 |isbn=0-89871-361-7 |location=Philadelphia, PA, USA |pages=34 |oclc=1348374386}}</ref>