User:Alexathkust/temp

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[edit] theorem 7.3

Let T be a linear operator on a finite-dimensional vector space V such that the characteristic polynomial of T splits, and let λ₁,λ₂,...,λ_k be the distinct eigenvalues of T. Then, for every , there exist vectors , such that

Proof
m: multiplicity of λ₁ or λ_i f(t): characteristic polynomial of T.

mathematic induction.

1.)k=1,(T-λI)^m=0

[edit] counter example

differentiable but partial derivative not continuous: http://www.math.umn.edu/~rogness/mathlets/partialsNotContDiff.html
not continuous at (0,0) http://www.math.tamu.edu/~tvogel/gallery/node14.html