Matrix addition

, adding two matrices would have the geometric effect of applying each matrix transformation separately onto

[1] 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 A + B, is computed by adding corresponding elements of A and B:[2][3] Or more concisely (assuming that A + B = C):[4][5] For example: Similarly, it is also possible to subtract one matrix from another, as long as they have the same dimensions.

In particular, the direct sum of square matrices is a block diagonal matrix.

denotes the k-by-k identity matrix then the Kronecker sum is defined by:

Illustration of the addition of two matrices.