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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
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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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

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