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Recall that any monic complex polynomial p € C[X] can be factorized into a prod- uct II-1 (1-c;)", of powers of linear p
Posted: Fri Apr 29, 2022 10:42 am
by answerhappygod
- Recall That Any Monic Complex Polynomial P C X Can Be Factorized Into A Prod Uct Ii 1 1 C Of Powers Of Linear P 1 (65.99 KiB) Viewed 42 times
Recall that any monic complex polynomial p € C[X] can be factorized into a prod- uct II-1 (1-c;)", of powers of linear polynomials 1 - c; for some distinct complex roots C1,C2,...,CHE C of "multiplicities" mı, m2, ..., MK E N respectively. Furthermore the roots Cj together with their assoicated multiplicities mi in such a factorization are unique up to a permutation of the list C1,C2, ..., C. Prove that for any A E M. (C), if its char- acteristic polynomial has a factorization pa II- (1 -
) as described above, then det (A) = II - (C;))