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

, antieigenvalue theory was developed by

Karl Gustafson Karl Edwin Gustafson is an American mathematician. Gustafson spent most of his career at the University of Colorado, Boulder, in the Department of Mathematics. He is known for developing the antieigenvalue theory in applied mathematics. Educ ...

from 1966 to 1968. The theory is applicable to

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statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

and

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

. 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