Elliot, David L. (1961) A Note on Systems of Linear Equations. SIAM Review, 3 (1). pp. 66-69. ISSN 0036-1445. doi:10.1137/1003006. https://resolver.caltech.edu/CaltechAUTHORS:20120921-104034855
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Abstract
This note is a comment on reference [1] and a generalization of the method there presented. We consider a system of m linear equations in n unknowns x_1, x_2,...x_n (1) Σ^(n)_(j=1) a_(ij)x_j = c_i i=1, 2,...m, a_(ij), c_i real or A∙x=c in matrix notation. We distinguish three cases: (I) There is no finite vector x satisfying (1) (inconsistent case); (II) There is a unique vector x satisfying (1); (III) There are an infinity of vectors x satisfying (1), such that their endpoints lie on some line, plane, or higher-dimensional linear manifold.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1961 SIAM. Received by the editors August 10, 1959. | |||||||||
| Issue or Number: | 1 | |||||||||
| DOI: | 10.1137/1003006 | |||||||||
| Record Number: | CaltechAUTHORS:20120921-104034855 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120921-104034855 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 34279 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | INVALID USER | |||||||||
| Deposited On: | 21 Sep 2012 19:31 | |||||||||
| Last Modified: | 09 Nov 2021 23:07 |
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