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Linear Algebra pp 201-245 | Cite as

Diagonalization

  • Jin Ho Kwak
  • Sungpyo Hong

Abstract

Gaussian elimination plays a fundamental role in solving a system Ax = b of linear equations. In general, instead of solving the given system, one could try to solve the normal equation A T Ax = A T b, whose solutions are the true solutions or the least squares solutions depending on whether or not the given system is consistent. Note that the matrix A T A is a symmetric square matrix, and so one may assume that the matrix in the system is a square matrix. For this kind of reason, we focus on a diagonal matrix or a linear transformation from a vector space to itself throughout this chapter.

Keywords

General Solution Recurrence Relation Characteristic Polynomial Linear Differential Equation Companion Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Jin Ho Kwak
    • 1
  • Sungpyo Hong
    • 1
  1. 1.Department of MathematicsPohang University of Science and TechnologyPohang, KyungbukSouth Korea

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