Matrix Multiply

For this challenge, we'll implement matrix multiplication using SQL.

Matrices are very important data structures in linear algebra. They are basically a grid of numbers, i.e. a 2D array. They can have varying "height" and "width," though we usually call those dimensions m and n respectively, i.e. a matrix has m rows and n columns.

For example, here are 2 matrices named A and B.

A is a 2×4 matrix, i.e. m = 2 and n = 4, and B is a 4×3 matrix.

Before we can multiply matrices, we need a way of representing a matrix in a SQL table. A good way to do that is to establish coordinates for the individual values in the matrix. We'll call these coordinates (i, j), where i is the row position and j is the columns position. So, we can use 1 row in a SQL table to represent 1 value in a matrix, where the row contains i, j, and value. Since we want to store multiple matrices in our table, we also want a name column to identify the different matrices.

To see how to multiply 2 matrices, I recommend this illustration on Wikipedia.

For the example matrices A and B above:

For this challenge, compute A × B for the matrices in the matrices table. The output should have the same representation as the input matrices, except that it doesn't need a name.