Trigonometric functions of matrices: Difference between revisions

Revision as of 10:08, 27 February 2016

Revision as of 12:30, 27 February 2016

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==Other functions==

The tangent, as well as [[inverse trigonometric functions]], [[hyperbolic function|hyperbolic]] and [[inverse hyperbolic function]]s have also been defined for matrices.:<ref>[https://help.scilab.org/docs/5.5.2/en_US/section_99038107015b1d789de50bf92f154a85.html Scilab trigonometry].</ref>

:<math>

\arcsin X = -i \ln \left( iX + \sqrt{I-X^2} \right)</math> (see [[Inverse trigonometric functions#Logarithmic forms]], [[Matrix logarithm]], [[Square root of a matrix]])

:<math>

\begin{align}

\sinh X & = {e^X - e^{-X} \over 2} \\

\cosh X & = {e^X + e^{-X} \over 2}

\end{align}

</math>

etc.

==References==