O mica generalizare
Posted: Wed Jun 04, 2008 1:20 pm
Fie \( A \in \mathcal{M}_n(\mathbb{C}) \) cu valorile proprii distincte \( x_1,x_2,...,x_n \). Demonstrati ca are loc egalitatea:
\( \sum_{k=1}^nrang(A-x_kI)=n(n-1) \).
\( \sum_{k=1}^nrang(A-x_kI)=n(n-1) \).