O problema cu matrice

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bogdanl_yex
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O problema cu matrice

Post by bogdanl_yex »

Fie \( A,B \in M_{n}(C) \) si \( \omega \) o radacina de ordinul \( p \) a unitatii. Aratati ca pentru orice matrice cu proprietatea ca \( AB= \omega BA \) are loc relatia \( (A+B)^{p}=A^{p}+B^{p} \).
"Don't worry about your difficulties in mathematics; I can assure you that mine are still greater"(Albert Einstein)
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Marius Mainea
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Post by Marius Mainea »

Se demonstreaza prin inductie dupa n relatia: \( (A+B)^n=A^n+(1+\omega+\omega^2+...+\omega^{n-1})\sum_{k=1}^{n-1}C_n^kA^{n-k}B^k+B^n \)
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