Algorithms for Hermite and Smith normal matrices and linear Diophantine equations
نویسندگان
چکیده
منابع مشابه
Hermite and Smith Normal Forms ofTriangular Integer Matrices
This paper considers the problem of transforming a triangular integer input matrix to canonical Hermite and Smith normal form. We provide algorithms and prove deterministic running times for both transformation problems that are linear (hence optimal) in the matrix dimension. The algorithms are easily implemented, assume standard integer multiplication, and admit excellent performance in practi...
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Hermite and Smith normal form are important forms of matrices used in linear algebra. These terms have many applications in group theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Hermite and Smith normal form of large dense matrices. The main problems of the c...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1971
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1971-0301909-x