Operator trigonometry of Hotelling correlation, Frobenius condition, Penrose twistor (Q1017636)

The author presents three new applications of his noncommutative operator trigonometry in matrix statistics, numerical analysis and theoretical physics, see \textit{K. Gustafson} [Operator Theory: Advances and Applications 167, 127--155 (2006; Zbl 1181.47007)] and references therein. He gives an operator-trigonometric proof of the inequality for the Hotelling correlation coefficient [\textit{S. Drury}, \textit{S. Liu}, \textit{C. Y. Lu}, \textit{S. Puntanen} and \textit{G. Styan}, Sankhya: The Indian Journal of Statistics Series A 64 (Pt. 2), 453--507 (2002)]. He states the operator-trigonometric meaning of the expression of \textit{F. Chaitin-Chatelin} and \textit{S. Gratton} [Numer. Linear Algebra Appl. 7, No.~5, 337--354 (2000; Zbl 1051.65052)] for the absolute condition number \(C(H)\) of the Hermitian polar factor \(H\) of a real invertible \(n\times n\) matrix, and also obtains a completely new operator trigonometry for twistor matrices.