Linear algebra help group

15 short videos in the Essence of linear algebra series by 3Blue1Brown on YouTube. First video is Vectors, what even are they?

Here is a simplified PCA code that we used on 6 March 2020: pca_code_part1.R (here’s the original code pca_code.R)

Here is code from Bryan Shader that illustrates how R does PCA: SVAPCA2.R

and an announcement … for the time-being we’re going to suspend our meetings due to the anticipated spread of COVID19. So there will be no meeting on 13 March 2020, nor during spring break (20 March). We will see from there and maybe we’ll get together via Zoom or something else thereafter.

Let’s follow up on this thread on Twitter, posted by a population genomicist at

Learning objectives

Linear algebra resources and links of interest

Online courses

Linear algebra

  • Khan Academy: Linear Algebra

    • Not really a stand alone linear algebra class (more as a supplement), but contains lots of good information.

  • Open Courseware: Linear Algebra

    • MIT’s introductory linear algebra course.

  • Open Courseware: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

    • The follow-on course to the introduction linear algebra class. Matrix methods expands on the fundamental concepts discussed and introduces some additional ideas that are also very useful, such as positive-definite matrices, singular value decomposition, etc.

  • Linear Algebra Courses

    • Free (or paid, if you want a certificate), self-paced linear algebra courses from a number of institutions.

Singular Value Decomposition (SVD)

SVD is a fundamental factorization technique that is used a in wide variety of situations and fields that vary from statistics (e.g., principal component analysis) to fluid flow (e.g., dynamical systems).

Principal Component Analysis (PCA)

A specific application of SVD focused on finding the rotation of a matrix that maximizes the most variation along a set of axes (columns) that have been standardized.

Videos highlighting applications of linear algebra

In addition to the 3Blue1Brown series, there are other videos and series out there that may be useful in illustrating the applications of linear algebra. Below are a couple of examples.