Matrix multiplication (GEMM): definition

Beginner

Multiplying two grids of numbers to make a third. Each box in the answer is a long row of multiplications added up.

Novice

$C = AB$ , where $A$ is $M \times K$ and $B$ is $K \times N$ . Every one of the $M \times N$ outputs is a sum of $K$ products, so it takes $MNK$ multiply-adds. GEMM (general matrix multiply) is the library name for it.

Expert

$2MNK$ FLOPs over $MK + KN + MN$ values, so its intensity grows with the smallest dimension. With $M = 1$ it degenerates to a matrix-vector product (GEMV), which is always memory-bound.