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

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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.

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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