# Multiplication of block/partitioned matrices

Put content here**Theorem.** Block matrices can be multiplied as if the blocks were scalar entries, provided the block dimensions are compatible.
⏎
If $A$ and $B$ are partitioned conformally:
$$A = \begin{pmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{pmatrix}, \quad B = \begin{pmatrix} B_{11} & B_{12} \\ B_{21} & B_{22} \end{pmatrix}$$
then:
$$AB = \begin{pmatrix} A_{11}B_{11} + A_{12}B_{21} & A_{11}B_{12} + A_{12}B_{22} \\ A_{21}B_{11} + A_{22}B_{21} & A_{21}B_{12} + A_{22}B_{22} \end{pmatrix}$$
⏎
The column partitioning of $A$ must match the row partitioning of $B$ for the block products to be defined.

# Parents

* Block matrices