This brings us to the end of the journey that we undertook. We began with taking weighted sums of numbers. We ended with Singular Value Decomposition. We also encountered some practical problems on our way.

Fill the gaps

However, there are a few topics we did not cover in this series. So the next thing you could do is read up on one or more of these topics:

• Solving linear equations using linear algebra
• LU decomposition
• Gram-Schmidt orthogonalization
• Left and right pseudo-inverses
• Determinants

Pick a direction to learn more

Another option is to learn a new field from a linear algebraic point of view. Some examples are:

• Spectral graph theory (my favorite and top pick): it connects graphs with linear algebra.
• (Discrete) Fourier transforms: it studies a particular class of orthogonal matrices and the interpretation of the matrix-vector product.
• Multi-variable calculus, vector calculus.

Pick a direction to build more

Yet another option is to apply the skills you have acquired so far to build stuff related to topics like:

• Computer graphics
• Machine learning
• Compression and how jpeg files use it
• Graph-based tools

I hope you enjoyed this series of visual essays.

← 24. Dimension reduction