Trigonometric functions of matrices: Difference between revisions

Revision as of 15:59, 2 March 2016

Revision as of 16:01, 2 March 2016

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\end{align}

</math>

with <math>X^n</math> being the {{mvar|n}}-th [[Matrix multiplication#Powers of matrices|power]] of the matrix {{mvar|X}}, and {{mvar|I}} being the [[identity matrix]] of appropriate dimensions.

with <math>X^n</math> being the <math>n</math>-th [[Matrix multiplication#Powers of matrices|power]] of the matrix <math>X</math> and <math>I</math> being the [[identity matrix]] of appropriate dimensions. Equivalently, they can be defined using the [[matrix exponential]] along with the matrix equivalent of [[Euler's formula]], <math>e^{iX} = \cos X + i \sin X</math>, yielding

:<math>

\begin{align}