Accession Number : AD0604174

Title :   AN INTRODUCTION AND BEGINNER'S GUIDE TO MATRIX PSEUDO-INVERSES,

Corporate Author : ARCON CORP LEXINGTON MASS

Personal Author(s) : Albert,Arthur

Report Date : JUL 1964

Pagination or Media Count : 73

Abstract : This paper presents a tutorial development of the theory of matrix pseudo-inverses, with some applications. The proofs are based on two classical theorems - the diagonalization theorem for symmetric matrices and the projection theorem for finite dimensional vector spaces. With the aid of the pseudo-inverse concept, explicit closed form expressions for such things as the general solution to under specified linear equations, the projection of a vector onto a linear manifold, the solution to least squares problems subject to linear constraints and the Gramm-Schmidt orthogon alization procedure are exhibited. An asymptotic expansion of (A + epsilon B) to the minus 1 power, where A is non-negative definite, B is positive definite and epsilon is small (the classical perturbation problem) which does not require knowledge of the eigenvalues and eigenvectors of A and B is developed. Briefly the definition of the pseudoinverse evolves as follows: If H is an n x M matrix and Z is an n-vector, there may or may not be an M-vector X, satisfying the equation HX = Z.

Descriptors :   (*MATRICES(MATHEMATICS), TRANSFORMATIONS (MATHEMATICS)), (*TRANSFORMATIONS (MATHEMATICS), MATRICES(MATHEMATICS)), PROJECTIVE GEOMETRY, LEAST SQUARES METHOD, PERTURBATION THEORY, EQUATIONS, THEOREMS

Distribution Statement : APPROVED FOR PUBLIC RELEASE