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
Canonical name	ExampleOfTraceOfAMatrix
Date of creation	2013-03-22 13:33:20
Last modified on	2013-03-22 13:33:20
Owner	Daume (40)
Last modified by	Daume (40)
Numerical id	8
Author	Daume (40)
Entry type	Example
Classification	msc 15A99