# [SOLVED]show V=Cx iff there are no multiple eigenvalue

#### chickenwin

##### New member
$L: V\to V$ a diagonalizable linear operator on finite-dim vector space.

show that $V = C_x$ iff there are no multiple eigenvalues

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here $C_x = \operatorname{span} \{x, L(x), L^2(x), \cdots\}$

basically it is a cyclic subspace generated by x that belongs to V.

edit: solved

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