# Antieigenvalue theory

The antieigenvectors $x$ are the vectors most turned by a matrix or operator $A$. 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.