Εκφώνηση
Να βρεθούν όλοι οι πίνακες $\Gamma=\biggl ( \Gamma_{ij} \biggr ) $
με στοιχεία $\Phi_{ij} \in \mathit{R}$ ώστε $A \cdot X=X \cdot A$
όπου $A=\begin{pmatrix}
1 & 2 \\
2 & 4
\end{pmatrix}$
Λύση
$$
A \cdot X = X \cdot A \iff
\begin{pmatrix}
X_{11} & X_{12} \\
X_{21} & X_{22}
\end{pmatrix}
\iff
\begin{pmatrix}
X_{11}-X_{21} & X_{12}-X_{22} \\
2X_{11}+4X_{21} & 2X_{12}+4X_{22}
\end{pmatrix} \nonumber
$$
$$
\begin{cases}
X_{11}-X_{21}&=X_{11}+2X_{12}\\
X_{12}-X_{22}&=X_{11}+4X_{12}\\
2X_{11}+4X_{21}&=X_{21}+2X_{22}\\
2x_{12}&=-2X_{21}
\end{cases}\nonumber
$$
$$
\left\{
\begin{aligned}
X_{11}-X_{21}&=X_{11}+2X_{12}\\
X_{12}-X_{22}&=X_{11}+4X_{12}\\
2X_{11}+4X_{21}&=X_{21}+2X_{22}\\
2x_{12}&=-2X_{21}
\end{aligned}\nonumber
\right .
$$
Η παράσταση:
$$y=\sum_{i=0}^{\infty} {a+i \over b+i}$$
$$
e^x=\lim_{n\to\infty} \left (1=\frac{x}{n} \right ) ^{n}
$$