Linear Dependence: Theory and Computation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2000
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Deals with the most basic notion of linear algebra, to bring emphasis on approaches to the topic serving at the elementary level and more broadly. A typical feature is where computational algorithms and theoretical proofs are brought together. Another is respect for symmetry, so that when this has some part in the form of a matter it should also be reflected in the treatment. Issues relating to computational method are covered. These interests may have suggested a limited account, to be rounded-out suitably. However this limitation where basic material is separated from further reaches of the subject has an appeal of its own. To the 'elementary operations' method of the textbooks for doing linear algebra, Albert Tucker added a method with his 'pivot operation'. Here there is a more primitive method based on the 'linear dependence table', and yet another based on 'rank reduction'. The determinant is introduced in a completely unusual upside-down fashion where Cramer's rule comes first. Also dealt with is what is believed to be a completely new idea, of the 'alternant', a function associated with the affine space the way the determinant is with the linear space, with n+1 vector arguments, as the determinant has n. Then for affine (or barycentric) coordinates we find a rule which is an unprecedented exact counterpart of Cramer's rule for linear coordinates, where the alternant takes on the role of the determinant. These are among the more distinct or spectacular items for possible novelty, or unfamiliarity. Others, with or without some remark, may be found scattered in different places |
| Beschreibung: | 1 Online-Ressource (XV, 175 p) |
| ISBN: | 9781461542735 9781461369196 |
| DOI: | 10.1007/978-1-4615-4273-5 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4615-4273-5 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461542735 9781461369196 |
| language | English |
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| spelling | Afriat, S. N. Verfasser aut Linear Dependence Theory and Computation by S. N. Afriat Boston, MA Springer US 2000 1 Online-Ressource (XV, 175 p) txt rdacontent c rdamedia cr rdacarrier Deals with the most basic notion of linear algebra, to bring emphasis on approaches to the topic serving at the elementary level and more broadly. A typical feature is where computational algorithms and theoretical proofs are brought together. Another is respect for symmetry, so that when this has some part in the form of a matter it should also be reflected in the treatment. Issues relating to computational method are covered. These interests may have suggested a limited account, to be rounded-out suitably. However this limitation where basic material is separated from further reaches of the subject has an appeal of its own. To the 'elementary operations' method of the textbooks for doing linear algebra, Albert Tucker added a method with his 'pivot operation'. Here there is a more primitive method based on the 'linear dependence table', and yet another based on 'rank reduction'. The determinant is introduced in a completely unusual upside-down fashion where Cramer's rule comes first. Also dealt with is what is believed to be a completely new idea, of the 'alternant', a function associated with the affine space the way the determinant is with the linear space, with n+1 vector arguments, as the determinant has n. Then for affine (or barycentric) coordinates we find a rule which is an unprecedented exact counterpart of Cramer's rule for linear coordinates, where the alternant takes on the role of the determinant. These are among the more distinct or spectacular items for possible novelty, or unfamiliarity. Others, with or without some remark, may be found scattered in different places Mathematics Information theory Electronic data processing Algebra Matrix theory Numeric Computing Applications of Mathematics Theory of Computation Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Mathematik Lineare Abhängigkeit (DE-588)4403103-8 gnd rswk-swf Lineare Abhängigkeit (DE-588)4403103-8 s 1\p DE-604 https://doi.org/10.1007/978-1-4615-4273-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Afriat, S. N. Linear Dependence Theory and Computation Mathematics Information theory Electronic data processing Algebra Matrix theory Numeric Computing Applications of Mathematics Theory of Computation Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Mathematik Lineare Abhängigkeit (DE-588)4403103-8 gnd |
| subject_GND | (DE-588)4403103-8 |
| title | Linear Dependence Theory and Computation |
| title_auth | Linear Dependence Theory and Computation |
| title_exact_search | Linear Dependence Theory and Computation |
| title_full | Linear Dependence Theory and Computation by S. N. Afriat |
| title_fullStr | Linear Dependence Theory and Computation by S. N. Afriat |
| title_full_unstemmed | Linear Dependence Theory and Computation by S. N. Afriat |
| title_short | Linear Dependence |
| title_sort | linear dependence theory and computation |
| title_sub | Theory and Computation |
| topic | Mathematics Information theory Electronic data processing Algebra Matrix theory Numeric Computing Applications of Mathematics Theory of Computation Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Mathematik Lineare Abhängigkeit (DE-588)4403103-8 gnd |
| topic_facet | Mathematics Information theory Electronic data processing Algebra Matrix theory Numeric Computing Applications of Mathematics Theory of Computation Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Mathematik Lineare Abhängigkeit |
| url | https://doi.org/10.1007/978-1-4615-4273-5 |
| work_keys_str_mv | AT afriatsn lineardependencetheoryandcomputation |