Editing Characteristic polynomial (section)

==Examples==

To compute the characteristic polynomial of the matrix
<math display=block>A = \begin{pmatrix}
2 & 1\\
-1& 0
\end{pmatrix}.
</math>
the [[determinant]] of the following is computed:
<math display=block>t I-A = \begin{pmatrix}
t-2&-1\\
1&t-0
\end{pmatrix}
</math> 
and found to be <math>(t-2)t - 1(-1) = t^2-2t+1 \,\!,</math> the characteristic polynomial of <math>A.</math>

Another example uses [[hyperbolic function]]s of a [[hyperbolic angle]] &phi;.
For the matrix take
<math display=block>A = \begin{pmatrix} \cosh(\varphi) & \sinh(\varphi)\\ \sinh(\varphi)& \cosh(\varphi) \end{pmatrix}.</math>
Its characteristic polynomial is
<math display=block>\det (tI - A) = (t - \cosh(\varphi))^2 - \sinh^2(\varphi) = t^2 - 2 t \ \cosh(\varphi) + 1 = (t - e^\varphi) (t - e^{-\varphi}).</math>