Matrix Algebra Review

In this video, ‪@centerstat‬ instructors Patrick Curran & Dan Bauer provide a review of matrix algebra concepts and operations that commonly appear in multivariate statistics. It is important to have some familiarity with matrix algebra when learning and applying multivariate models for several reasons: models are often expressed in matrix notation, software often references model matrices in output, and some things in multivariate statistics are really best understood with reference to matrix operations. In this video, 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.
An annotated copy of the slides to accompany this video can be downloaded from centerstat.org/matrix-review/

[@dougcheung3817]

Patrick is an amazing teacher. I took his CenterStat's free course on intro to SEM and it was life changing (no affiliations declared).

[@aun3931]

A much needed one!
Many want to 'do' multivariate statistics but few want to pick a book about matrices.

[@Ivaniushina]

Thank you so much for clear explanation

[@shidnng72]

Thank you, you’re truly gifted teachers! Attended several of Centerstat workshops and highly recommend EVERY ONE of them 🙌
Also, you really should consider the „Quantitube“-idea 😆😂

[@centerstat]

thanks so much for your kind words...we have lots of fun doing these, and it beats working at our day jobs. Good luck with your work -- Patrick

[@larissacury7714]

Hi, thanks very very much for this, it helped me a lot to get an overall understanding of matrix algebra. I started to study matrix algebra because I already know how to perform and interpret regression models (in R, mostly), but now I'd like to go a step further and really understand what is going on behind the scenes to improve my understanding of them and of other models. Do you have tips on how could I do this? I mean, from a beginner's perspective, what resources may I use in order to understand matrix algebra so that I can apply to my existing knowledge of stats and futher expand it? (I don't come com a math background).

[@centerstat]

Good morning -- thanks for your note and your kind words. I think having a foundational knowledge in matrix algebra is hugely helpful when applying a variety of statistical models to real data. It both helps you understand what the models are doing, but also what is happening when things go wrong. Unfortunately, it's challenging to find general introductions because things tend to get very complicated, very quickly. Often you can get a good presentation of this in a classic multivariate statistics class, or maybe a factor analysis class. Also, there are many (many) tutorials on UA-cam, some of which are better than others. One of my favorite is at Kahn Academy -- they do great work in everything they do. I hope you find this helpful -- take care -- patrick