Hermite and Smith Normal Forms ofTriangular Integer Matrices
نویسنده
چکیده
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 practice. The results presented here lead to faster practical algorithms for computing the Hermite and Smith normal form of an arbitrary (non triangular) integer input matrix.
منابع مشابه
Lectures on Integer Matrices
Introduction 2 Lecture 1. Hermite and Smith normal forms 3 Lecture 2. Integral similarity and the Latimer-MacDuffee-Taussky theorem 8 Lecture 3. Ideal class numbers, integral matrices nonderogatory modulo every prime and maximal orders of number fields 12 Lecture 4. Factorizations of integer matrices as products of elementary matrices, involutions etc 20 Lecture 5. Additive commutators. Solving...
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