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sir descrescator si chiar 0 de la un rang incolo cu ranguri

 
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Cezar Lupu
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Joined: 26 Sep 2007
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Location: Pittsburgh/Craiova/Bucharest/Constanta

PostPosted: Sat May 21, 2011 10:56 am    Post subject: sir descrescator si chiar 0 de la un rang incolo cu ranguri Reply with quote

Fie A\in M_{n}(\mathbb{R}) si definim sirul a_{k}=rang(A^{k+1})-rang(A^k), k\geq 0. Sa se arate ca:

a) sirul a_{k} este descrescator;

b) sirul a_{k} este egal cu 0 de la un anumit moment dat.
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Last edited by Cezar Lupu on Mon Jun 13, 2011 8:27 pm; edited 1 time in total
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Theodor Munteanu
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Joined: 06 May 2008
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Location: Sighetu Marmatiei/Bucharest

PostPosted: Sun May 22, 2011 11:55 pm    Post subject: Reply with quote

a_k \leq 0 deci cf a) nu ar putea fi 0 decat daca ar fi constant
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