- Tytuł:
- About a certain relation between two polynomials of the same degree
- Autorzy:
- Piwowarczyk, T.
- Powiązania:
- https://bibliotekanauki.pl/articles/229447.pdf
- Data publikacji:
- 2011
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
roots of polynomials
symmetric polynomials
companion matrix
eigenvalues
transformations - Opis:
- This article presents several different methods for solving the problem of how to find a certain relation defined in chapter 2. The first method deals with the identities known in the theory of symmetric polynomials as the elements of a certain vector space. The second method is designed around the matrix transformations between symmetric polynomials. The third method is designed around the property of a linear operator and its characteristic polynomial. The fourth method is designed in the area of complex numbers, and introduces the multiplication group of 'complex roots of one'. Significant improvement in the third and fourth method is made by introducing so called 'block method'. It facilitates all calculations by making them much shorter. The article ends with an example showing symmetry and regularity of all procedures. Finally, the article shows how to solve the problem for any degree n of the polynomial, and for any degree k. At the end of the paper solutions for n < 5 and k < 5 are tabulated.
- Źródło:
-
Archives of Control Sciences; 2011, 21, 1; 85-103
1230-2384 - Pojawia się w:
- Archives of Control Sciences
- Dostawca treści:
- Biblioteka Nauki
Artykuł