Mathematics-Online course: Linear Algebra-Matrices-Matrix Operations-The Vector Space of Matrices

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	Mathematics-Online course: Linear Algebra - Matrices - Matrix Operations
	The Vector Space of Matrices

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The $m\times n$ -matrices form a vectorspace, that is, they can be added and they can be multiplied by scalars. These operations are defined componentwise:

$\displaystyle C = A+B$	$\displaystyle \Leftrightarrow$	$\displaystyle c_{i,j} = a_{i,j}+b_{i,j},$
$\displaystyle B = \lambda A$	$\displaystyle \Leftrightarrow$	$\displaystyle b_{i,j} = \lambda a_{i,j}\, .$

(Authors: Burkhardt/Höllig/Hörner)

automatically generated 4/21/2005