Matrix addition
The usual
matrix addition is defined for two
matrices of same dimensions.
The
sum of two
m-by-
n matrices
A and
B, denoted by
A + B, is again an
m-by-
n matrix computed by adding corresponding elements, i.e.,
(
A + B)[
i, j] =
A[
i, j] +
B[
i, j]. For example
The
m ×
n matrices with matrix addition as operation form an
abelian group.
For any arbitrary matrices A (of size m × n) and B (of size p × q) , we have the direct sum of A and B, denoted by and defined as
For instance,