Abstract
Although in general the minimum polynomial of a linear mapping f : Vā V can be expressed as a product of powers of irreducible polynomials over the ground field F of V, say \( {m_f} = \mathop p\nolimits_1^{{e_1}} \mathop p\nolimits_2^{{e_2}} ...\mathop p\nolimits_k^{{e_k}} \), the irreducible polynomials p i need not be linear. Put another way, the eigenvalues of f need not belong to the ground field F. It is therefore natural to seek a canonical matrix representation for f in the general case, which will reduce to the Jordan representation when all the eigenvalues of f do belong to F. In order to develop the machinery to deal with this, we first consider the following notion.
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Ā© 2002 Springer-Verlag London Limited
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Blyth, T.S., Robertson, E.F. (2002). Rational and Classical Forms. In: Further Linear Algebra. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0661-6_7
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DOI: https://doi.org/10.1007/978-1-4471-0661-6_7
Publisher Name: Springer, London
Print ISBN: 978-1-85233-425-3
Online ISBN: 978-1-4471-0661-6
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