Mathematics-Online lexicon: Expansion Theorem for Determinants

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	Mathematics-Online lexicon:
	Expansion Theorem for Determinants

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 determinant of an $n\times n$ -matrix

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

-th row and the

-th column of

(Authors: Burkhardt/Höllig/Hörner)

Annotation:

Proof: Expansion Theorem for Determinants

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automatically generated 2/10/2005