On the Smith normal form of Varchenko matrix
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 کاملOn Efficient Sparse Integer Matrix Smith Normal Form Computations
We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo powers of word-size primes. Consequently, the algorithm does not suffer from coefficient growth. We have implemented several variants of this algorithm (Elimination and/or Black-Box techniques) since...
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...
متن کاملThe Smith Normal Form Distribution of A Random Integer Matrix
We show that the density μ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities μps of SNF over Z/p sZ with p a prime and s some positive integer. Our approach is to connect the SNF of a matrix with the greatest common divisors (gcds) of certain polynomials of matrix entries, and develop the theory of multi-gcd distribution of polynomial values at a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2020
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.2262.9b8