Denote the sum of two matrices 
and 
(of the same dimensions) by 
. The sum is defined by adding entries with the same indices
 |
over all 
and 
.
For example,
![[a_(11) a_(12); a_(21) a_(22)]+[b_(11) b_(12); b_(21) b_(22)]=[a_(11)+b_(11) a_(12)+b_(12); a_(21)+b_(21) a_(22)+b_(22)].](/images/equations/MatrixAddition/NumberedEquation2.svg) |
Matrix addition is therefore both commutative and associative.
Matrix Addition
See also
Matrix, Matrix MultiplicationExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Matrix Addition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MatrixAddition.html