PlanetMath: example of trace of a matrix

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example of trace of a matrix

(Example)

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

$\displaystyle \operatorname{trace}(A+B)$	$\displaystyle = \operatorname{trace}(A) + \operatorname{trace}(B)$
	$\displaystyle = (2 + 10 + 18) + (9 + 5 + 1)$
	$\displaystyle = 45$

$\displaystyle \operatorname{trace}(A)$	$\displaystyle = \operatorname{trace}(2A')$
	$\displaystyle = 2\cdot \operatorname{trace}(A')$
	$\displaystyle = 2\cdot \operatorname{trace} \left[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}right]$
	$\displaystyle = 2\cdot (1 + 5 + 9)$
	$\displaystyle = 30$

"example of trace of a matrix" is owned by Daume.

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This is version 5 of example of trace of a matrix, born on 2003-04-05, modified 2004-04-14.
Object id is 4160, canonical name is ExampleOfTraceOfAMatrix.
Accessed 5086 times total.

Classification:

AMS MSC:

15A99 (Linear and multilinear algebra; matrix theory :: Miscellaneous topics)

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