 Matrix multiplication

Since a matrix $M$ can be seen as a linear map $f_M(\vec{x})$, the product of two matrices $MN$ can be seen as the composition of two linear maps:One cool thing about linear functions is that we can easily pre-calculate this product only once to obtain a new matrix, and so we don't have to do both multiplications separately each time.

Matrix multiplication is a mathematical operation that takes two matrices and produces a third matrix. The multiplication of matrices is not as straightforward as multiplying individual numbers because specific rules govern when and how matrices can be multiplied together. Here are the key points about matrix multiplication: 1. **Compatibility**: To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.