The Penrose-Moore Pseudo Inverse with Diverse Statistical Applications. Part I. The General Theory and Computational Methods.

The Penrose-Moore Pseudo Inverse extends the notion of inverse for square nonsingular matrices to the class of all rectangular matrices. In the report the author develops the essential properties with applications to the theory of equations, constrained and unconstrained least squares, nonnegative definiteness, perturbation theory and the singular decomposition theorem. Various computational algorithms are developed and additional results are derived which apply to various statistical topics, such as the General Linear Hypothesis BLUES, Orthogonal Designs, tests and confidence sets Conditional Expectations for vector normal variables and Kalman Filtering. Author