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.