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On some properties of trigonometric matrices. (English) Zbl 0642.34024
The pair of $$n\times n$$ matrices $$\{$$ S(x),C(x)$$\}$$ which satisfy $$Y'=Q(x)Z$$, $$Z'=-Q(x)Y$$ and the initial conditions $$S(a)=0$$, $$C(a)=E$$, where E is the $$n\times n$$ identity matrix and Q(x) is an $$n\times n$$ symmetric matrix of continuous functions on [a,$$\infty)$$, are called trigonometric matrices. These matrices have been used to study the self- adjoint matrix differential system $$(F(x)Y')'+G(x)Y=0$$ by means of the generalized Prüfer transformation. In this paper, the author studies oscillation properties of trigonometric matrices and extend some well- known trigonometric formulae to trigonometric matrices.
Reviewer: N.Parhi

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations