MATRIX TRIGONOMETRY

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