Subiectul 1, Concursul centrelor de excelenta 2008

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Bogdan Cebere
Thales
Posts: 145
Joined: Sun Nov 04, 2007 1:04 pm

Subiectul 1, Concursul centrelor de excelenta 2008

Post by Bogdan Cebere »

Fiind date matricele \( A,B \in M_3(R) \), sa se arate relatia: \( |\det (A+iB)|^2=\det (A^2+B^2)-\tr ((BA-AB)^*(A^2+B^2)). \)
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Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Folosim relatia: \( det(A+xB)=detBx^3+tr(AB^\ast)x^2+mx+detA \)

pentru \( A\mapsto(A^2+B^2)\ \ \ B\mapsto i(BA-AB) \)
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