Problema 2 ONM 2008
Posted: Thu May 01, 2008 8:31 am
Demonstrati ca o matrice inversabila \( A\in \mathcal{M}_n(\mathbb{C}) \) are proprietatea \( A^{-1}=\overline{A} \) daca si numai daca exista o matrice inversabila \( B \in \mathcal{M}_n(\mathbb{C}) \) a.i. \( A=B^{-1}\cdot \overline{B} \) (matricea \( \overline{A} \) este matricea A cu elementele complex conjugate )
Vasile Pop, ONM 2008; Moubinool Omarjee, IMC 2002 (detalii aici)
Vasile Pop, ONM 2008; Moubinool Omarjee, IMC 2002 (detalii aici)