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A Note on Systems of Linear Equations

Elliot, David L. (1961) A Note on Systems of Linear Equations. SIAM Review, 3 (1). pp. 66-69. ISSN 0036-1445. http://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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/1003006DOIUNSPECIFIED
http://epubs.siam.org/doi/abs/10.1137/1003006PublisherUNSPECIFIED
Additional Information:© 1961 SIAM. Received by the editors August 10, 1959.
Record Number:CaltechAUTHORS:20120921-104034855
Persistent URL:http://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: Jason Perez
Deposited On:21 Sep 2012 19:31
Last Modified:26 Dec 2012 16:14

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