ABSTRACT
The notion of a generalized inverse of a matrix has its origin in the theory of simultaneous linear equations. Any matrix A has at least one generalized inverse, which is a matrix G such that Gb is a solution to a set of consistent linear equations Ax = b (Rao and Mitra, 1971). We give the definition and properties of generalized inverses of matrices in section 3.1, while in section 3.2, we discuss solutions to systems of linear equations. Section 3.3 describes unconstrained and constrained optimization. These topics are fundamental in the development of linear model theory.
