ABSTRACT
This chapter considers inverses of matrices which play a similar role to reciprocals of scalars. It deals with the inverse of a square matrix which has full rank since this is the easiest and most commonly occurring case in routine statistical applications. The chapter begins with definitions, examples (including in R) and basic properties before looking at some tricks for handling matrices which have various patterns. It considers partitioned matrices. It is particularly useful in both linear models and in multivariate analysis when variables might divide into distinct groups and so it is convenient to partition the design matrix or the data matrix to reflect these groups. This may lead to interpreting the variance matrix as composed of blocks down the diagonal, giving the variance matrices of the subgroups of variables and the off-diagonal blocks as covariances between variables in different groups.
