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det (a AB + b BA + c I_2) = det (a BA + b AB + c I_2)

 
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Mateescu Constantin
Newton


Joined: 21 Apr 2009
Posts: 398
Location: Londra/Pitesti

PostPosted: Tue Sep 28, 2010 7:51 pm    Post subject: det (a AB + b BA + c I_2) = det (a BA + b AB + c I_2) Reply with quote

Aratati ca pentru orice matrici A{\normal\ ,\ }B\in\mathcal{M}_2(\mathbb{R}) si pentru orice numere complexe

a{\normal\ ,\ }b{\normal\ ,\ }c avem : \det\ (aAB+bBA+cI_2)=\det\ (aBA+bAB+cI_2) .

Vasile Pop, shortlist 2006
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Marius Mainea
Gauss


Joined: 26 May 2008
Posts: 1099
Location: Gaesti (Dambovita)

PostPosted: Wed Sep 29, 2010 12:55 am    Post subject: Reply with quote

Folosim

\det(A+B)=\det A+tr(AB^{\ast})+\det B
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