Daca \( A,B\in M_n(\mathbb{C}) \) si \( A \) comuta cu \( AB-BA \) , aratati ca \( AB-BA \) nilpotenta.
Kaplansky
O problema cu matrice a lui Kaplansky
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opincariumihai
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opincariumihai
- Thales
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- Joined: Sat May 09, 2009 7:45 pm
- Location: BRAD
A se vedea problema 3 de aicibae wrote:Problema s-a dat anul acesta la IMC.
Last edited by opincariumihai on Sun Oct 04, 2009 5:31 pm, edited 1 time in total.
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Beniamin Bogosel
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Ideea e simpla si logica: sa consideram urmele puterilor lui \( AB-BA \) si sa observam ca sunt toate egale cu 0.
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