Matrix product ($AB$)

For matrices $A\in {\mathbb{F}}^{m\times n}$ and $B\in {\mathbb{F}}^{n\times p}$, their matrix product is the matrix $AB\in {\mathbb{F}}^{m\times p}$ with entries $(AB{)}_{ij}={\sum }_{k=1}^n{A}_{ik}{B}_{kj}$. The operation producing it is matrix multiplication, representing composition of the corresponding linear maps.