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Orthonormal and Unitary Transformations

  • Tom Lyche
Chapter
  • 196 Downloads
Part of the Texts in Computational Science and Engineering book series (TCSE, volume 22)

Abstract

In Gaussian elimination and LU factorization we solve a linear system by transforming it to triangular form. These are not the only kind of transformations that can be used for such a task. Matrices with orthonormal columns, called unitary matrices can be used to reduce a square matrix to upper triangular form and more generally a rectangular matrix to upper triangular (also called upper trapezoidal) form. This lead to a decomposition of a rectangular matrix known as a QR decomposition and a reduced form which we refer to as a QR factorization. The QR decomposition and factorization will be used in later chapters to solve least squares- and eigenvalue problems.

References

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    G.H. Golub, C.F. Van Loan, Matrix Computations, 4th Edition (The John Hopkins University Press, Baltimore, MD, 2013)zbMATHGoogle Scholar
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    G.W. Stewart, Matrix Algorithms Volume I: Basic Decompositions (SIAM, Philadelphia, 1998)CrossRefGoogle Scholar
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    J.H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Tom Lyche
    • 1
  1. 1.Blindern, University of OsloOsloNorway

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