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Expansion Theorem for Determinants


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The determinant of an $ n\times n$-matrix $ A$ can be expanded by any row or column:

\begin{displaymath}
\begin{array}{rcll}
\operatorname{det} A &=&
\sum\limits...
...{i,l} &
(\text{expansion\ by\ column}\ l)\,
,
\end{array}
\end{displaymath}

where $ \tilde A_{i,j}$ denotes the matrix we obtain by deleting the $ i$-th row and the $ j$-th column of $ A$.

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  automatisch erstellt am 19.  8. 2013