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| Format: | Artículo científico |
| Language: | en |
| Published: |
Universidad Nacional Autónoma de México
2007
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| Online Access: | https://www.redalyc.org/articulo.oa?id=40480406 |
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Table of Contents:
- Solution of Rectangular Systems of Linear Equations Using Orthogonalization and Projection Matrices M. A. Murray Lasso Ingeniería dyads Gram Schmidt process linear vector spaces orthogo nal pro jec tion matrices Rectangular systems of linear equations In this paper a novel approach to the solution of rectangular systems of linear equations is presented. It starts with a homogeneous set of equations and through linearsespace con siderations obtains the solution by finding the null space of the coefficientmatrix. To do this an or thogonal basis for the row space of the coefficient matrix isfound and this basis is completed for the whole space using the GramSchmidtorthogonalization process. The non homogeneous case is handled by converting theproblem into a homogeneous one, passing the right side vector to the left side, lettingthe components of the negative of the right side be come the coefficients of and additional variable, solving the new system and at the end imposing the condition that theadditional variable take a unit value.It is shown that the null space of the coefficient matrix is intimately connected with orthogonal projection matrices which are easily constructed from the or thogonalbasis using dyads. The paper treats the method introduced as an exact method when the originalcoefficients are rational and rational arithmetic is used. The analysis of the efficiencyand numerical characteristics of the method is de ferred to a future paper. De tailed numerical illustrative examples are provided in the paper and the use of the programMathematica to perform the computations in rational arithmeticis illustrated. 2007 artículo científico 1405-7743 https://www.redalyc.org/articulo.oa?id=40480406 en http://www.redalyc.org/revista.oa?id=404 Ingeniería. Investigación y Tecnología application/pdf Universidad Nacional Autónoma de México Ingeniería. Investigación y Tecnología (México) Num.4 Vol.VIII