The geometrical meaning of the Kantorovich–Wielandt inequalities Original Research Article

The Kantorovich–Wielandt angle θ(A) and the authorʹs operator angle φ(A) are related by cos φ(A2)=sin θ(A). Here A is an arbitrary symmetric positive definite (SPD) matrix. The relationship of these two different geometrical perspectives is discussed. An extension to arbitrary nonsingular matrices A is given. A related four-way relationship with the operator trigonometry, strengthened CBS constants, and domain decomposition methods is noted.