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In [[applied mathematics]], '''antieigenvalue theory''' was discovered by [[Karl Gustafson]] from 1966 to 1968. The theory is applicable to [[numerical analysis]], [[wavelet]]s, [[statistics]], [[quantum mechanics]], [[finance]] and [[optimization]]. 

The antieigenvectors <math>x</math> are the vectors most turned by a matrix or operator <math>A</math>. The corresponding antieigenvalue <math>\mu</math> is the cosine of the maximal turning angle. The maximal turning angle is <math>\phi(A)</math> and is called the angle of the operator. Just like the eigenvalues which may be ordered as a spectrum from smallest to largest, the theory of antieigenvalues orders the antieigenvalues of an operator A from the smallest to the largest turning angles.

The theory of antieigenvalues addresses the stability problem of eigenvalues.{{clarify|date=February 2013}}

==References==
<div class="references">

*{{Citation | last1=Gustafson | first1=Karl | title=The angle of an operator and positive operator products | doi=10.1090/S0002-9904-1968-11974-3  | mr=0222668  | year=1968 | journal=[[Bulletin of the American Mathematical Society]] | issn=0002-9904 | volume=74 | issue=3 | pages=488–492 | zbl=0172.40702 }}
* {{Citation
| last=Gustafson
| first=Karl
| title=Antieigenvalue Analysis
| publisher=World Scientific
| year=2012
| url=http://www.worldscibooks.com/mathematics/8247.html
| isbn=978-981-4366-28-1
| zbl=
}}.

[[Category:Operator theory]]
[[Category:Matrix theory]]