A Bird’s-Eye View of Linear Algebra: Matrix Chain Multiplication

This is the fourth chapter of the in-progress book on linear algebra. The table of contents so far:

• Chapter-1: The basics
• Chapter-2: The measure of a map — determinants
• Chapter-3: Why is matrix multiplication the way it is?
• Chapter-4 (current): Matrix chain multiplication
• Chapter-5: Systems of equations, linear regression and neural networks
• Chapter-6: Rank nullity and why row rank == col rank

We covered matrix multiplication in chapter 3 and why it is defined the way it is. We also visualized the operation in five different ways. It was worth spending a chapter on this very important operation since it is so fundamental in so many fields.

And where there are two matrices, there are soon many. One of the matrices in a matrix multiplication will often split into two and so on until we get a whole chain of matrices to be multiplied together. And unlike with two matrices, where there is only one, it turns…