Extending Pseudo Inverses for Matrices to Linear Operators in Hilbert Space

Abstract

In this paper formulas derived by the author for calculating the pseudo inverse of any matrix are generalized to linear operators in Hilbert space. The pseudo inverse is seldom required unless there are many right side vectors, which become known at differet times. The minimum square solution of functional equations is also presented for a single right-side vector. Some definitions and theorems of functional analysis are included. An application to a simple minimum energy optimal contol problem is presented in detail.