Polynomials for the Jordan decomposition in characteristic p
نویسندگان
چکیده
منابع مشابه
Characteristic Polynomials of p-adic Matrices
We analyze the precision of the characteristic polynomial χ(A) of an n × n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p), we give a criterion (checkable in time O (̃n)) for χ(A) to have precision exactly O(p). We also give a O (̃n) algorithm for determining the optimal precision when the criterion is not satisfied, and give examp...
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15 صفحه اولCharacteristic Polynomials
Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...
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LetK be a field of characteristic p > 0 equipped with a valuation v : K∗ → G taking values in an ordered abelian group G. Let OK = {α ∈ K : v(α) ≥ 0} and mK = {α ∈ K : v(α) > 0} be the valuation ring and maximal ideal, respectively, and suppose that the residue field OK/mK is finite, with q elements. Theorem 1. If f(x) = a0x n0 + a1x n1 + · · · + akxk is a polynomial with k + 1 nonzero coeffici...
متن کاملJordan Matrix Decomposition
We follow the rules: i, j, m, n, k denote natural numbers, K denotes a field, and a, λ denote elements of K. Let us consider K, λ, n. The Jordan block of λ and n yields a matrix over K and is defined by the conditions (Def. 1). (Def. 1)(i) len (the Jordan block of λ and n) = n, (ii) width (the Jordan block of λ and n) = n, and (iii) for all i, j such that 〈i, j〉 ∈ the indices of the Jordan bloc...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.05.012