Trigonometric functions of matrices: Difference between revisions

Revision as of 17:42, 26 February 2016

Revision as of 23:30, 26 February 2016

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If <math>X</math> is a [[diagonal matrix]], <math>\sin X</math> and <math>\cos X</math> are also diagonal matrices with <math>(\sin X)_{nn} = \sin( X_{nn})</math> and <math>(\cos X)_{nn} = \cos (X_{nn})</math>, that is, they can be calculated by simply taking the sines or cosines of the matrice's diagonal components.

The analogs of the [[trigonometric addition formulas]] holdare astrue well[[if and only if]] <math>XY = YX</math>:<ref name="Higham" />

:<math>

\begin{align}