Matrix addition

In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together.

For a vector, ${\displaystyle {\vec {v}}\!}$, adding two matrices would have the geometric effect of applying each matrix transformation separately onto ${\displaystyle {\vec {v}}\!}$, then adding the transformed vectors.

${\displaystyle \mathbf {A} {\vec {v}}+\mathbf {B} {\vec {v}}=(\mathbf {A} +\mathbf {B} ){\vec {v}}\!}$

However, there are other operations that could also be considered addition for matrices, such as the direct sum and the Kronecker sum.