1)let A be a matrix of n*n above K. let P be a polynom of K[x] such that the polynom P = 0 when substituting A into that polynom. What can we say about the eigenvalues of A? What can we say about matrices that has one or more of these eigenvalues? can we say that this polynom is zero when substituting one of these eigenvalues? (well , I am 99& sure about it since I read this proof).(adsbygoogle = window.adsbygoogle || []).push({});

2)(Test question) Let T be a linear transformation from V to V , when dimV is finite. ||T*(V)||<=||T(V)|| for all v E V, I need to proof that T is normal. Now , obviously we need to proof that ||T*(V)||=||T(V)|| because then we get (after playing with both sides of the equation: (v,TT*v)<=(v,T*Tv).

Now I don't think that its possible that T* can be such transformation that makes the vector shorter each times (But its probably just intuition I developed from this question). I tried to come up with a sentence or something logical for it but I failed.

Well that's for now, Its kinda simple and basic I guess, but I am stuck and I really need help.

Thanks,

Aviv

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# Many little linear questions

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