In this chapter, we covered linear algebra techniques in R. Unlike many of the prior chapters, many of the methods covered in this chapter do not produce an interesting result that has a substantive interpretation. Rather, these methods can be used to build numerical algorithms as shown in the final two examples. We covered linear algebra operations, including transposition, inversion, matrix multiplication, and a number of matrix transformations. We then went on to explore how these methods can be applied in Rasch analysis, internal consistency, and image compression. The subsequent chapters will focus on linear algebra's use in dealing with covariance matrices to perform principal component analysis, factor analysis, and structural equation modeling.