Extending Pseudo Inverses for Matrices to Linear Operators in Hilbert Space
| Autor: | M. A. Murray-Lasso |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Pure mathematics
Mathematical analysis Ingeniería Hilbert space General Engineering Pseudo inverse operators Spectral theorem Operator theory Square (algebra) minimum norm optimization linear operators Matrix (mathematics) symbols.namesake Simple (abstract algebra) symbols discretization Operator norm Moore–Penrose pseudoinverse Mathematics |
| Zdroj: | Universidad Nacional Autónoma de México UNAM Redalyc-UNAM Journal of Applied Research and Technology (México) Num.3 Vol.9 |
| ISSN: | 2448-6736 1665-6423 |
| DOI: | 10.22201/icat.16656423.2011.9.03.437 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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