Exact reduction of a polynomial matrix to the Smith normal form
نویسندگان
چکیده
منابع مشابه
The Smith Normal Form of a Matrix
In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...
متن کاملThe Smith Normal Form of a Matrix
In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...
متن کاملA local construction of the Smith normal form of a matrix polynomial
We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular row and column operations to the origina...
متن کاملA Fast Las Vegas Algorithm for Computing the Smith Normal Form of a Polynomial Matrix
A Las Vegas probabilistic algorithm is presented that finds the Smith normal form S ∈ Q[x] of a nonsingular input matrix A ∈ Z [x]. The algorithm requires an expected number of O (̃nd(d + n log ||A||)) bit operations (where ||A|| bounds the magnitude of all integer coefficients appearing in A and d bounds the degrees of entries of A). In practice, the main cost of the computation is obtaining a ...
متن کاملThe Smith normal form of a specialized Jacobi-Trudi matrix
Let JTλ be the Jacobi-Trudi matrix corresponding to the partition λ, so det JTλ is the Schur function sλ in the variables x1, x2, . . . . Set x1 = · · · = xn = 1 and all other xi = 0. Then the entries of JTλ become polynomials in n of the form ( n+j−1 j ) . We determine the Smith normal form over the ring Q[n] of this specialization of JTλ . The proof carries over to the specialization xi = q i...
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ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 1979
ISSN: 0018-9286
DOI: 10.1109/tac.1979.1102104