Elements of the Theory of Generalized Inverses of Matrices (Modules and Monographs in Undergraduate Mathematics and Its Applications)

Cline, R.E.

ISBN 10: 0817630139 / ISBN 13: 9780817630133

Editore: Birkhäuser, 1979

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Codice articolo ERICA77308176301396

Dati bibliografici

• Titolo: Elements of the Theory of Generalized Inverses of Matrices (Modules and Monographs in Undergraduate Mathematics and Its Applications)
• Editore: Birkhäuser
• Data di pubblicazione: 1979
• Lingua: Inglese
• ISBN 10: 0817630139
• ISBN 13: 9780817630133
• Rilegatura: Paperback
• Condizione: Very Good
• Tipo di libro: book

Descrizione articolo

Riassunto

At the suggestion of the UMAP Editor, the approach in the present monograph is (1) to develop the material in terms of full rank factoriza­ tions and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) to include an appendix of hints for exercises.

Contenuti

1. Introduction.- 1.1 Preliminary Remarks.- 1.2 Matrix Notation and Terminology.- 1.3 A Rationale for Generalized Inverses.- 2. Systems of Equations and the Moore-Penrose Inverse of a Matrix.- 2.1 Zero, One or Many Solutions of Ax = b.- 2.2 Full Rank Factorizations and the Moore-Penrose Inverse.- 2.3 Some Geometric Illustrations.- 2.4 Miscellaneous Exercises.- 3. More on Moore-Penrose Inverses.- 3.1 Basic Properties of A+.- 3.2 Applications with Matrices of Special Structure.- 3.3 Miscellaneous Exercises.- 4. Drazin Inverses.- 4.1 The Drazin Inverse of a Square Matrix.- 4.2 An Extension to Rectangular Matrices.- 4.3 Expressions Relating Ad and A+.- 4.4 Miscellaneous Exercises.- 5. Other Generalized Inverses.- 5.1 Inverses That Are Not Unique.- Appendix 1: Hints for Certain Exercises.- Appendix 2: Selected References.- Index to Principal Definitions.