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- Thread starter Fermat
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- Thread starter
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- Jan 29, 2012

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When you say

Do you mean thatI know eigenvectors corresponding to different eigenvalues are linearly independent

but asking, "what if there are more than two?". One can show generally, "if, in a set of vectors, any two are independent (au+ bv= 0 only if a= b= 0 which is the same as saying that b is NOT a multiple of a and vice-versa) then all the vectors are independent."but what about a set ${e_{1},...,e_{n}}$ of eigenvectors corresponding to different eigenvalues?

One can prove that by first proving 'if [tex]u_1, u_2, ... u_n[/tex] are each independent of v, then so is [tex]a_1u_1+ a_2u_2+ ...+ a_nu_n[/tex] is independent of v for any numbers [tex]a_1[/tex], [tex]a_2[/tex], ..., [tex]a_n[/tex].