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Essential Mathematics for Applied Fields pp 437–460Cite as

Systems of Linear Equations and Generalized Inverse

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Abstract

A useful application of the results of the preceding Section will now be made. We will consider first the general solutions to systems of linear homogeneous equations, and then that of systems linear non-homogeneous equations. These results will then be used in finding a so-called generalized inverse of a matrix.

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References to Additional and Related Material: Section 16

  1. Ben-Israel, A. and T. Greville, “Generalized Inverses: Theory and Applications”, Wiley and Sons, Inc., New York (1974).

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  2. Bose, R., Unpublished Lecture Notes, University of North Carolina at Chapel Hill (1964).

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  3. Boullion, T. and P. Odell, “Generalized Inverse Matrices”, Wiley-Interscience, (1971).

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  4. Cullen, C., “Matrices and Linear Transformations”, Addison-Wesley, Inc. (1966).

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  5. Johnston, J., “Linear Equations and Matrices”, Addison-Wesley, Inc. (1966).

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  6. Pease, M., “Methods of Matrix Algebra”, Academic Press (1965).

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  7. Pipes, L., “Matrix Methods for Engineers”, Prentice-Hall, Inc. (1963).

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  8. Paige, L. and O. Taussky (Editors), “Simultaneous Linear Equations and the Determination of Eigenvalues”, National Bureau of Standards, Applied Mathematics Series No. 29, Washington, D. C. (1953).

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  9. Pringle, P. and A. Rayner, “Generalized Inverse Matrices with Applications to Statistics”, Griffin Monograph 28 (1971).

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  10. Rao, C. and S. Mitra, “Conditional Inverse of Matrices and its Applications”, John Wiley and Sons, Inc. (1971).

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  11. Wilkenson, J. and C. Reinsch, “Linear Algebra”, Springer-Verlag, New York (1971).

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Authors and Affiliations

  1. Niagara University, College of Arts and Sciences, Niagara University, New York, 14109, USA

    Richard M. Meyer

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  1. Richard M. Meyer
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© 1979 Springer-Verlag New York Inc.

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Meyer, R.M. (1979). Systems of Linear Equations and Generalized Inverse. In: Essential Mathematics for Applied Fields. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8072-6_16

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  • DOI: https://doi.org/10.1007/978-1-4613-8072-6_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90450-4

  • Online ISBN: 978-1-4613-8072-6

  • eBook Packages: Springer Book Archive

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