8. Other resources

Table of contents

  1. Khan Academy
  2. 3Blue1Brown
  3. Mathematics for Machine Learning
  4. Linear Algebra for Data Science

The links below are more detailed than our guides, covering lots of important ideas we didn’t touch on above (and won’t get a chance to cover in Practical Data Science).

Khan Academy

For more depth and added explanations, take a look at Khan Academy’s linear algebra course. Specifically, look at:

  1. All of Unit 1: Vectors and spaces.
  2. The first four lessons in Unit 2: Matrix transformations, through Inverse functions and transformations.
  3. The first two lessons in Unit 3: Alternate coordinate systems (bases), through Orthogonal projections. Understanding the content of the orthogonal projections lesson is the primary learning objective of these guides.

In addition, look at Khan Academy’s Multivariable calculus course, specifically:

  1. Most of Unit 1: Thinking about multivariable functions, though the lesson on Visualizing vector-valued functions is not necessary.
  2. The first three lessons in Unit 2: Derivatives of multivariable functions, through Partial derivative and gradient. (These are also linked above.)

3Blue1Brown

Grant Sanderson (3Blue1Brown) produces excellent visual explanations of a lot of ideas that are central to data science, including neural networks, but also linear algebra. His Essence of Linear Algebra series overlaps a fair bit with the videos we’ve provided above, but with some content missing (namely, projecting onto the span of multiple vectors) and other content more heavily emphasized (e.g. the idea of a linear transformation). The series exists in two forms:

Either way, (at least) the first 9 chapters are relevant to us.

Mathematics for Machine Learning

Mathematics for Machine Learning, by Garrett Thomas, is a document that discusses the mathematics relevant for machine learning in much greater detail than we’ll need in this course. It’s quite advanced, so don’t be alarmed if the material there feels inaccessible. (More of it will make sense after Practical Data Science!)

Linear Algebra for Data Science

If you’d prefer to read a more formal textbook on these ideas, take a look at Linear Algebra for Data Science by Wanmo Kang and Kyunghyun Cho (a PDF is available at the linked site). Specifically, read Chapters 1-4.