
Accession Number : AD0604174
Title : AN INTRODUCTION AND BEGINNER'S GUIDE TO MATRIX PSEUDOINVERSES,
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 pseudoinverses, 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 pseudoinverse 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 GrammSchmidt orthogon alization procedure are exhibited. An asymptotic expansion of (A + epsilon B) to the minus 1 power, where A is nonnegative 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 nvector, there may or may not be an Mvector 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