Cramer-type Formula for the Polynomial Solutions of Coupled Linear Equations with Polynomial Coefficients | Zendy

Tateaki Sasaki | Zendy

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Cramer-type Formula for the Polynomial Solutions of Coupled Linear Equations with Polynomial Coefficients

Author(s) -

Tateaki Sasaki

Publication year - 1985

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195179845

Subject(s) - mathematics , reciprocal polynomial , polynomial , matrix polynomial , stable polynomial , monic polynomial , type (biology) , wilkinson's polynomial , alternating polynomial , pure mathematics , mathematical analysis , ecology , biology

This paper derives a determinant form formula for the general solution of coupled linear equations with coefficients in K[XI, xn], where K is a field of numbers, the number of unknowns is greater than the number of equations, and the solutions are in K(x\, ..., Xn-i)[xn]The formula represents the general solution by the minimum number of generators, and it is a generalization of Cramer's formula for the solutions in K ( X I , ..., xn)Compared with another formula which is obtained by a method typical in algebra, the generators in our formula are represented by determinants of quite small orders. §

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