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https://elib.psu.by/handle/123456789/31537| Title: | Characteristic and Minimal Polynomials In Problems |
| Authors: | Kazak, Y. Ehilevsky, S. Gurieva, N. |
| Issue Date: | 2019 |
| Publisher: | Полоцкий государственный университет |
| Citation: | Kazak, Y. Characteristic and Minimal Polynomials In Problems / Y. Kazak, S. Ehilevsky, N. Gurieva // European and National Dimension in Research = Европейский и национальный контексты в научных исследованиях : electronic collected materials of XI Junior Researcher' Conference, Novopolotsk, May 23-24, 2019 : in 3 parts / Ministry of Education of Belarus, Polotsk State University ; ed. D. Lazouski [et al.]. - Novopolotsk : PSU, 2019. - Part 3 : Technology. - P. 201-203. |
| Abstract: | In linear algebra, the minimal polynomial of an n-by-n matrix A over a field F is the monic polynomial p(x) over F of least degree such that p(A)=0. Any other polynomial q with q(A)=0 is a (polynomial) multiple of p. The following three statements are equivalent: ??F is a root of p(x), ? is a root of the characteristic polynomial of A, ? is an eigenvalue of A. The multiplicity of a root ? of p(x) is the geometric multiplicity of ? and is the size of the largest Jordan block corresponding to ? and the dimension of the corresponding Eigen space. The minimal polynomial is not always the same as the characteristic polynomial. |
| URI: | https://elib.psu.by/handle/123456789/31537 |
| Appears in Collections: | European and National Dimension in Research. Technology. 2019 |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| 201-203.pdf | 171.67 kB | Adobe PDF | View/Open |
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