Matrix multiplication ↩

Metadata

aliases: [MatMul]
shorthands: {}
created: 2021-12-04 15:50:36
modified: 2022-01-12 16:19:50

Matrix multiplication is a binary operation that produces a matrix from two matrices. For it to be possible, the number of columns in the first matrix must be equal to the number of rows in the second matrix, as shown by this image:

We know that matrices represent linear maps, so what does matrix multiplication represent? It represents the composition of linear maps.

Definition

Let be an and be an matrix.

And have their product be , an matrix:

In index form: