Fie \( A=(a_{ij}) \) o matrice \( n\times n \) cu elemente reale astfel incat
i) \( a_{ii}>0,\ 1\leq i\leq n \),
ii) \( a_{ij}\leq 0,\ 1\leq i, j\leq n,\ i\neq j \),
iii) \( \sum_{i=1}^{n}a_{ij}>0,\ 1\leq j\leq n \).
Aratati ca \( \det(A)>0 \).
Matrice cu determinantul strict pozitiv
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Matrice cu determinantul strict pozitiv
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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Aplicatie a teoremei Gershgorin .
http://planetmath.org/encyclopedia/Gers ... eorem.html
http://planetmath.org/encyclopedia/Gers ... eorem.htmlA mathematician is a machine for turning coffee into theorems.