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Jordan Canonical Form

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Linear Algebra

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

This chapter is of a distinctly more difficult nature than the preceding ones. In it will treat the problem of finding a particular simple canonical, or normal, matrix representative of a linear transformation. In the preceding chapter we treated this problem for self-adjoint linear transformations in a finite-dimensional inner product space. For a finite-dimensional inner product space V and a self-adjoint linear transformation

$$ T:v \to v $$

we saw that we could always find an orthonormal basis for V such that the corresponding matrix of T was diagonal. The required basis would be composed of the normed eigenvectors of T, and the diagonal entries of the corresponding matrix are the eigenvalues of T. The problem to be considered here is Can we achieve a similar normal form in general? One answer to this question leads to the Jordan canonical form, also called the Jordan normal form. Before we arrive at this goal we will require quite a few preparatory steps.

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© 1998 Springer Science+Business Media New York

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Smith, L. (1998). Jordan Canonical Form. In: Linear Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1670-4_17

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  • DOI: https://doi.org/10.1007/978-1-4612-1670-4_17

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7238-0

  • Online ISBN: 978-1-4612-1670-4

  • eBook Packages: Springer Book Archive

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