# example of trace of a matrix

Let $A=\left[\begin{array}[]{ccc}2&4&6\\ 8&10&12\\ 14&16&18\end{array}\right]$, $A^{\prime}=\frac{1}{2}A=\left[\begin{array}[]{ccc}1&2&3\\ 4&5&6\\ 7&8&9\end{array}\right]$ and $B=\left[\begin{array}[]{ccc}9&8&7\\ 6&5&4\\ 3&2&1\end{array}\right]$ then

 $\displaystyle\operatorname{trace}(A+B)$ $\displaystyle=\operatorname{trace}(A)+\operatorname{trace}(B)$ $\displaystyle=(2+10+18)+(9+5+1)$ $\displaystyle=45$
 $\displaystyle\operatorname{trace}(A)$ $\displaystyle=\operatorname{trace}(2A^{\prime})$ $\displaystyle=2\cdot\operatorname{trace}(A^{\prime})$ $\displaystyle=2\cdot\operatorname{trace}\left[\begin{array}[]{ccc}1&2&3\\ 4&5&6\\ 7&8&9\end{array}\right]$ $\displaystyle=2\cdot(1+5+9)$ $\displaystyle=30$
Title example of trace of a matrix ExampleOfTraceOfAMatrix 2013-03-22 13:33:20 2013-03-22 13:33:20 Daume (40) Daume (40) 8 Daume (40) Example msc 15A99