diagonala principala a unei matrice

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Cezar Lupu
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diagonala principala a unei matrice

Post by Cezar Lupu »

Pe diagonala principala a unei matrice \( A\in M_{n}(\mathbb{C}) \) se gasesc radacinile de ordin \( n \) ale unitatii. Sa se demonstreze ca exista
matrice \( B, C\in M_{n}(\mathbb{C}) \) astfel incat \( B+C=A \), \( B^{n}=I_{n} \) si \( C^{n}=O_{n} \).


Jozseph Wildt International Contest, 2005
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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