applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...

, antieigenvalue theory was developed by

Karl Gustafson Karl may refer to: People * Karl (given name), including a list of people and characters with the name * Karl der Große, commonly known in English as Charlemagne * Karl Marx, German philosopher and political writer * Karl of Austria, last Austri ...

from 1966 to 1968. The theory is applicable to

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

wavelet A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...

and

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

. The antieigenvectors

x

are the vectors most turned by a matrix or operator

A

, that is to say those for which the angle between the original vector and its transformed image is greatest. The corresponding antieigenvalue

\mu

is the cosine of the maximal turning angle. The maximal turning angle is

\phi(A)

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.

References

* * . Operator theory Matrix theory {{mathapplied-stub