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

For a vector, then adding the transformed vectors.

Definition

Two matrices must have an equal number of rows and columns to be added. In which case, the sum of two matrices A and B will be a matrix which has the same number of rows and columns as A and B. The sum of A and B, denoted , is computed by adding corresponding elements of A and B:

Or more concisely (assuming that ):

For example:

Similarly, it is also possible to subtract one matrix from another, as long as they have the same dimensions. The difference of A and B, denoted , is computed by subtracting elements of B from corresponding elements of A, and has the same dimensions as A and B. For example:

See also

• Matrix multiplication

• Vector addition

• Direct sum of matrices

• Kronecker sum

Notes

References