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Mathematics-Online lexicon:

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 1/27/2005