Trigonometric functions of matrices: Difference between revisions

Revision as of 02:27, 26 December 2018

Revision as of 20:43, 3 March 2019

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{{Use American English|date = March 2019}}

The trigonometric functions (especially [[sine]] and [[cosine]]) for real or complex [[square matrices]] occur in solutions of second-order systems of [[differential equation]]s.<ref>{{cite journal|title=Efficient Algorithms for the Matrix Cosine and Sine|authors=Gareth I. Hargreaves, Nicholas J. Higham|journal=Numerical Analysis Report|issue=461|publisher=Manchester Centre for Computational Mathematics|year=2005}}</ref> They are defined by the same [[Taylor series]] that hold for the trigonometric functions of real and [[complex numbers]]:<ref name="Higham">{{cite book|title=Functions of matrices: theory and computation|author=Nicholas J. Higham|year=2008|pages=287f|isbn=9780898717778}}</ref>

{{Short description|Important functions in solving differential equations}}

The '''trigonometric functions''' (especially [[sine]] and [[cosine]]) for real or complex [[square matrices]] occur in solutions of second-order systems of [[differential equation]]s.<ref>{{cite journal|title=Efficient Algorithms for the Matrix Cosine and Sine|authors=Gareth I. Hargreaves, Nicholas J. Higham|journal=Numerical Analysis Report|issue=461|publisher=Manchester Centre for Computational Mathematics|year=2005}}</ref> They are defined by the same [[Taylor series]] that hold for the trigonometric functions of real and [[complex numbers]]:<ref name="Higham">{{cite book|title=Functions of matrices: theory and computation|author=Nicholas J. Higham|year=2008|pages=287f|isbn=9780898717778}}</ref>

:<math>\begin{align}