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Mathematics-Online course: Linear Algebra - Matrices - Determinants

Expansion of 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$.
(Authors: Burkhardt/Höllig/Hörner)

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  automatically generated 4/21/2005