In applied mathematics, antieigenvalue theory was developed by Karl Gustafson from 1966 to 1968. The theory is applicable to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization.
The antieigenvectors x are the vectors most turned by a matrix or operator A . The corresponding antieigenvalue μ is the cosine of the maximal turning angle. The maximal turning angle is ϕ ( 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.
The theory of antieigenvalues addresses the stability problem of eigenvalues.
