Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

An algorithm for the exact reduction of a matrix to Frobenius form using modular arithmetic. I


Author: Jo Ann Howell
Journal: Math. Comp. 27 (1973), 887-904
MSC: Primary 65F30
DOI: https://doi.org/10.1090/S0025-5718-1973-0378381-9
MathSciNet review: 0378381
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is in two parts. Part I contains a description of the Danilewski algorithm for reducing a matrix to Frobenius form using rational arithmetic. This algorithm is modified for use over the field of integers modulo p. The modified algorithm yields exact integral factors of the characteristic polynomial. A description of the single-modulus algorithm is given. Part II contains a description of the multiple-modulus algorithm. Since different moduli may yield different factorizations, an algorithm is given for determining which factorizations are not correct factorizations over the integers of the characteristic polynomial.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F30

Retrieve articles in all journals with MSC: 65F30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0378381-9
Keywords: Modular arithmetic, residue arithmetic, modulus, Frobenius form, Danilewski method, characteristic polynomial, similarity transformation, prime number, Chinese Remainder Theorem
Article copyright: © Copyright 1973 American Mathematical Society