ABSTRACT
This chapter provides an introduction to a few topics in matrix algebra which are unlikely to be considered in an early undergraduate level course on linear algebra but can be of immense practical use in certain statistical applications. It provides a collation of various further decompositions of matrices into factors of particular structures. The first of these is restricted to matrices of full column rank and the others are restricted to square matrices. These have application both in developing methodological techniques and in efficient numerical calculation of solutions of linear equations, eigenanalyses, determinants and inverses of non-singular matrices. The second topic is generalized inverses which extend the definition of an inverse beyond that of a non-singular square matrix. This has application in the analysis of linear models, particularly models where the design matrix is not of full rank. The third and fourth consider different forms of the product of two matrices, the Hadamard and Kronecker products.
