Vector and Matrix Algebra

Abstract

The statistical inference on parameters will be derived in linear models. A linear relation can be treated in a compact and lucid form by vectors and matrices, so that in the following, the definitions and theorems of linear algebra are introduced which will be needed later. The methods of vector spaces will also be discussed. They allow one to use geometric conceptions even then, when the spaces being used are of higher dimensions than the three-dimensional space we are familiar with. Finally, generalized inverses are discussed, by which one can easily change models of full rank for the estimation of parameters to models which are not full rank.