Matrix Transpose and Powers

The Transpose of $A$ ($A^T$) is the matrix whose columns are the rows of $A$:

${\left[\begin{array}{cccc}1& 2& 3& 4\\ 0& 1& 0& 2\end{array}\right]}^T=\left[\begin{array}{cc}1& 0\\ 2& 1\\ 3& 0\\ 4& 2\end{array}\right]$

Powers

$A^k=AA\dots A$

Properties

1. $(A^T{)}^T=A$
2. $(A+B{)}^T=A^T+B^T$
3. $(\mathbf{r}A{)}^T=\mathbf{r}{A}^T$
4. $(AB{)}^T=B^T{A}^T$