Abstract
A review of the principal ideal domain F[x] of all polynomials f(x) in the indeterminate x over the field F: degree f(x), evaluation mappings, the polynomial division law, the Euclidean algorithm for gcds. Irreducible polynomials p(x) over F, the extension field F(c) where p(c)=0.
Equivalence of s×t matrices A(x) over F[x], elementary row and column operations over F[x]. Reduction of A(x) to its Smith normal form S(A(x)), the invariant factors d l (x) of A(x). Calculation of invertible matrices P(x) and Q(x) over F[x] satisfying P(x)A(x)=Q(x)S(A(x)).
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© 2012 Springer-Verlag London Limited
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Norman, C. (2012). The Polynomial Ring F[x] and Matrices over F[x]. In: Finitely Generated Abelian Groups and Similarity of Matrices over a Field. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-2730-7_4
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DOI: https://doi.org/10.1007/978-1-4471-2730-7_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2729-1
Online ISBN: 978-1-4471-2730-7
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