1 V vector space (dim = n) and f End(V) nilpotent. Prove that dimV <= gr(mf). dim(ker f). 2 If M is a nxn matrix, prove that exists B a nxn matrix so that det(M+tB) is not 0 for all t different of 0.

(mf = minimal polinomial of f)

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- October 12th 2007, 12:01 PMkezmanLinear Algebra
1 V vector space (dim = n) and f End(V) nilpotent. Prove that dimV <= gr(mf). dim(ker f). 2 If M is a nxn matrix, prove that exists B a nxn matrix so that det(M+tB) is not 0 for all t different of 0.

(mf = minimal polinomial of f)