In math, factorization (British English: factorisation) or factoring is the decay of an entity (for example, a digit, a polynomial, or a matrix into a result of additional objects,...
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are called the "invariant factors" of T , and satisfy psi_i|psi_(i+1) for i=1 , ..., s-1 ( Hartwig 1996). The polynomial psi_s is the matrix minimal polynomial and the ...
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The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors. SEE ALSO: Rational Canonical ...
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Matrices - elementary transformations, Non-singular linear polynomials.
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Invariant factor - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Invariant_factor
The invariant factors of a matrix over a PID occur in the Smith normal form and provide a means of computing the structure of a module from a set of generators ... |
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Frobenius normal form - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Frobenius_normal_form
Given an arbitrary square matrix, the elementary divisors used in the construction of the Jordan normal form do not exist over F[x], so the invariant factors ai(x) as ...
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Let A be nxn matrix with entries in F[x]. Goal: Find a method to compute the invariant factors p1,…,pr. Suppose A is the companion matrix of a monic polynomial ...
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Two n-square matrices A and B over a field F are similar over a field F if and only if their characteristic matrices have the same invariant factors or the same rank ...
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matrices. Many researchers are interested in the invariant factors of these q- matrices. In this ... Applications of invariant factors of a q-matrix can be found in [3 ].
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34 INVARIANT FACTORS AND ELEMENTARY DIVISORS [ III]. The inverses of the matrices used in these transformations are. Pl} = 1 - 9%", QT} = Qua R“ = 1 + ...
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