A Polynomial Approach to Linear Algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1996
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research |
| Physical Description: | 1 Online-Ressource (XIII, 361 p) |
| ISBN: | 9781441987341 9780387946436 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4419-8734-1 |
Staff View
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| indexdate | 2024-07-10T01:21:04Z |
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| isbn | 9781441987341 9780387946436 |
| issn | 0172-5939 |
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| spelling | Fuhrmann, Paul A. Verfasser aut A Polynomial Approach to Linear Algebra by Paul A. Fuhrmann New York, NY Springer New York 1996 1 Online-Ressource (XIII, 361 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research Mathematics Matrix theory Systems theory Mathematical optimization Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Lineare Algebra (DE-588)4035811-2 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s 2\p DE-604 https://doi.org/10.1007/978-1-4419-8734-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fuhrmann, Paul A. A Polynomial Approach to Linear Algebra Mathematics Matrix theory Systems theory Mathematical optimization Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4123623-3 |
| title | A Polynomial Approach to Linear Algebra |
| title_auth | A Polynomial Approach to Linear Algebra |
| title_exact_search | A Polynomial Approach to Linear Algebra |
| title_full | A Polynomial Approach to Linear Algebra by Paul A. Fuhrmann |
| title_fullStr | A Polynomial Approach to Linear Algebra by Paul A. Fuhrmann |
| title_full_unstemmed | A Polynomial Approach to Linear Algebra by Paul A. Fuhrmann |
| title_short | A Polynomial Approach to Linear Algebra |
| title_sort | a polynomial approach to linear algebra |
| topic | Mathematics Matrix theory Systems theory Mathematical optimization Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Mathematics Matrix theory Systems theory Mathematical optimization Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Lineare Algebra Lehrbuch |
| url | https://doi.org/10.1007/978-1-4419-8734-1 |
| work_keys_str_mv | AT fuhrmannpaula apolynomialapproachtolinearalgebra |