Inegalitate cu determinant

Moderators: Bogdan Posa, Laurian Filip, Beniamin Bogosel, Radu Titiu, Marius Dragoi

Post Reply
opincariumihai
Thales
Posts: 134
Joined: Sat May 09, 2009 7:45 pm
Location: BRAD

Inegalitate cu determinant

Post by opincariumihai »

Fie \( A,B\in M_n(\mathbb{R}) \) astfel incat \( AB=O_n \). Demonstrati ca \( \det(A^2+B^2)\geq0 \).

Mihai Opincariu
Top
Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Folosind problema,

\( \det (A^2+B^2)=\det (A+B)^2\ge 0 \)
Top
Post Reply

Return to “Algebra”