Abstract
The goal of this chapter is a more complete study of linear transformations of a complex or real vector space to itself, including the investigation of nondiagonalizable transformations. The Jordan normal forms for complex and real vector spaces are established. The final part of the chapter contains applications of the Jordan normal form: raising a matrix to a power, analytic functions of matrices, solution of systems of linear differential equations with constant coefficients. Linear differential equations in the plane and their singular points are investigated in greater detail.
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- 1.
One may find a detailed proof in, for example, the book Lectures on Algebra, by D.K. Faddeev (in Russian) or in Sect. 3.4 of Matrix Analysis, by Roger Horn and Charles Johnson. See the references section for details.
- 2.
This name comes from the fact that if at some moment in time, a material point whose motion is described by system (5.48) is located at a singular point, then it will remain there forever.
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© 2012 Springer-Verlag Berlin Heidelberg
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Shafarevich, I.R., Remizov, A.O. (2012). Jordan Normal Form. In: Linear Algebra and Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30994-6_5
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DOI: https://doi.org/10.1007/978-3-642-30994-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30993-9
Online ISBN: 978-3-642-30994-6
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