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Matrix Addition

Denote the sum of two Matrices ${\hbox{\sf A}}$ and ${\hbox{\sf B}}$ (of the same dimensions) by ${\hbox{\sf C}}={\hbox{\sf A}}+{\hbox{\sf B}}$. The sum is defined by adding entries with the same indices

c_{ij} \equiv a_{ij}+b_{ij}

over all $i$ and $j$. For example,

\left[{\matrix{a_{11} & a_{12}\cr a_{21} & a_{22}\cr}}\right...
... & a_{12}+b_{12}\cr a_{21}+b_{21} & a_{22}+b_{22}\cr}}\right].

Matrix addition is therefore both Commutative and Associative.

See also Matrix, Matrix Multiplication

© 1996-9 Eric W. Weisstein