The geometrical meaning of the Kantorovich-Wielandt inequalities
The main results of this paper are Theorem 1. For any symmetric positive definite matrix \(A\), \[ \cos\phi(A^2)= \sin\theta(A), \] where \(\phi(A)\) is the Gustafson operator angle and \(\theta(A)\) is the Kantorovich-Wielandt angle. Theorem 2. For any symmetric positive definite matrix \(A\), \[ \phi^2(A)+ \theta(A)={\pi\over 2}. \] Theorem 3. \(\cos\phi(A^*A)= \sin\theta(A)\) for any nonsingular \(n\times n\) matrix \(A\).
scientific article; zbMATH DE number 1371432