Matrix Algebra Review: Video & Handouts

Recorded: November 4, 2022

Matrix algebra is used throughout all of multivariate statistics for a variety of purposes and having a foundational knowledge of matrices will help you learn new methods more quickly, empowering you to test hypotheses in ways not otherwise possible. For example, you will often see models presented in textbooks, manuscripts, and online resources using matrix notation. Presenting models in matrix form offers compactness and flexibility, where the rows and columns of the relevant matrices naturally expand or contract to fit the dimensions of the specific analysis (e.g., number of observations, number of predictors). Additionally, many software programs operate on matrices, even if this isn't obvious in the user interface or syntax structure. A "parser" operates behind the scenes, populating matrices that are used to define and fit the model. Why this matters to you is that sometimes the software will spit out a cryptic warning message like, "G Matrix is non-positive definite" (see this Help Desk post if you're curious about this one). You need to be able to decipher messages like this, know whether to worry about them, and have a sense of how to fix things when necessary. Finally, many things in statistics are really best (or only) understood using concepts of matrix algebra, such as leverage statistics in linear regression, eigenvector centrality in network analysis, component scores in principal components analysis, or how multidimensional scaling compresses individual differences across 10 variables into a two-dimensional plot. For all of these reasons, it is important to gain some familiarity with matrix algebra when learning more about multivariate statistics. In this Matrix Algebra Review, Patrick and Dan provide a guided tour of this foreign land, imparting conceptual meaning to matrix operations, offering humorous and semi-pertinent anecdotes, and occasionally bickering good naturedly with one another. We hope you will find this material to be of some use as you learn and apply multivariate statistics of various kinds.


Daniel J. Bauer, Ph.D.

Dan Bauer is a Professor and the Director of the L.L. Thurstone Psychometric Laboratory in the Department of Psychology and Neuroscience at the University of North Carolina. He teaches primarily graduate-level courses in statistical methods, for which he has won multiple teaching awards. Read More

Patrick J. Curran, Ph.D.

Patrick Curran is a Professor in the L.L. Thurstone Psychometric Laboratory in the Department of Psychology and Neuroscience at the University of North Carolina at Chapel Hill. He is dedicated to teaching and disseminating advanced quantitative methods and has won multiple awards for teaching excellence. Read More

Workshop Details


CenterStat workshops routinely receive excellent reviews.  Here is a sampling from our free 3-day structural equation modeling workshop:

Dan and Patrick do an awesome job at breaking down complex material and provide great applicable examples that really help with understanding and clarifying the concepts. The notes and materials provided are excellent and very detailed! 

The workshop had a relaxed environment with plenty of banter. It was easy to follow the step-by-step workshop. As a result, I was able to learn a lot in a short amount of time.

Clear examples, software demonstrations/code, nice pacing (I appreciated the background information!). I was also extremely impressed by how responsive Dan/Patrick/Ethan were to participant questions! 

Using real data to show examples and providing notes detailed for actually conducting the analyses later. The balance of what the theory is with the practical application is what my previous stats training often lacked (too little application).

The key strength was the clarity of communication and the balance between technicalities and intuition. Dr. Curran & Dr. Bauer did not shy away from technical aspects of the content but also communicated about them as intuitively as possible.

Dr. Curran and Dr. Bauer's style of lecture made complex statistical concepts straightforward and non-intimating, the lecture notes were very clear and the ability to ask questions via chat during lecture was amazing.  

I have a much better understanding of what data modeling is. Before the workshop, I knew how to do SEM and even wrote a paper currently under review using SEM, but I didn't really understand what I was doing, why I was doing it, how it was being done

High quality materials and explanations. Very engaging to listen to.

The instructors were incredible. The way they taught complex concepts made things that were difficult for me to grasp previously magically fall into place.  Concepts were clear and analogies were entertaining and on point!

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