Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online lexicon:


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

The sum of the diagonal elements of a $ n\times n$ matrix $ A$ is called trace of $ A$,

$\displaystyle \operatorname{trace}(A)=\sum_{i=1}^n a_{ii}\,.

For arbitrary $ (n \times n)$-matrices $ A, B$ we have

$\displaystyle \operatorname{trace}(AB) = \operatorname{trace}(BA) .$

Hence, for a regular matrix $ T$ and an arbitrary matrix $ A$ it follows, that

$\displaystyle \operatorname{trace}(T^{-1}AT) = \operatorname{trace}(A),$

which means that the trace is invariant under change of basis.

  automatically generated 4/20/2005