Matrix trigonometry Original Research Article

This paper brings up to date with new results a matrix trigonometry which I originated about twenty-five years ago. In particular, a new view of the construction and nature of antieigenvectors implicit within a minmax theorem is presented, new results showing that both antieigenvectors and eigenvectors satisfy the nonlinear Euler equation are given, and new implications for a combinatorial higher antieigenvector theory are illustrated in terms of numerical linear algebra.