Editing Function of a real variable (section)

==Matrix valued functions==

A [[matrix (mathematics)|matrix]] can also be a function of a single variable. For example, the [[rotation matrix]] in 2d:

:<math>
R(\theta) = \begin{bmatrix}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta \\
\end{bmatrix}</math>

is a matrix valued function of rotation angle of about the origin. Similarly, in [[special relativity]], the [[Lorentz transformation]] matrix for a pure boost (without rotations):

:<math>
\Lambda(\beta) = \begin{bmatrix}
\frac{1}{\sqrt{1-\beta ^2}} & -\frac{\beta }{\sqrt{1-\beta ^2}} & 0 & 0 \\
-\frac{\beta }{\sqrt{1-\beta ^2}} & \frac{1}{\sqrt{1-\beta ^2}} & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}</math>

is a function of the boost parameter ''β'' = ''v''/''c'', in which ''v'' is the [[relative velocity]] between the frames of reference (a continuous variable), and ''c'' is the [[speed of light]], a constant.