Moore-Penroseov matrični inverz : delo diplomskega seminarja

Matušek, Matic (author), Dolžan, David (mentor)

Moore-Penroseov matrični inverz, ali drugače psevdoinverz matrike, je posplošeni inverz za m×n matrike, ne nujno polnega ranga. Psevdoinverz je mogoče izračunati z različnimi metodami, v diplomskem delu pa se bom posvetil eni izmed njih, ki ne zahteva računanja lastnih vrednosti matrike. Na koncu si bomo še pogledali, kako nam ta metoda pomaga karakterizirati normalne matrike med EP matrikami.

• Language: Slovenian
• Keywords: posplošeni matrični inverz, Moore-Penroseov matrični inverz, psevdoinverz, normalna matrika, EP matrika
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-158957
• UDC: 512
• COBISS.SI-ID: 199744003
• Publication date in RUL: 23.06.2024

Secondary language

• Language: English
• Title: Moore-Penrose matrix inverse

Abstract

The Moore-Penrose matrix inverse or equivalently pseudoinverse is a generalized matrix inverse for m × n matrices, not necessarily of full rank. Pseudoinverse can be computed with many different methods. In this thesis I will concentrate on a method that does not require us to compute the eigenvalues. In the end, I will also explore how this method can help us characterize normal matrices among EP matrices.

• Keywords: generalized matrix inverse, Moore-Penrose matrix inverse, pseudoinverse, normal matrix, EP matrix