Accession Number : AD0724752

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

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Albert,Arthur

Report Date : 01 APR 1971

Pagination or Media Count : 111

Abstract : 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 (BLUE'S, Orthogonal Designs, tests and confidence sets) Conditional Expectations for vector normal variables and Kalman Filtering. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), ALGEBRAIC TOPOLOGY, VECTOR SPACES, COMPLEX VARIABLES, PROBABILITY, INEQUALITIES, LEAST SQUARES METHOD, SET THEORY, MAPPING(TRANSFORMATIONS), REGRESSION ANALYSIS, LINEAR PROGRAMMING, PERTURBATION THEORY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE