Day: October 5, 2012

Here is some quick note for the existence of eigenvector for linear operator $latex T$  in complex vector space of dimension $latex n$. Consider any non-zero vector $latex X$ in the space, we have the $latex n+1$ vectors $latex X, T[X],T^2[X],T^3[X],\cdots,T^n[X]$ to be linearly dependent. Thus, there exists $latex a_0,a_1,\cdots,a_n$ such that $latex a_0+a_1T[X]+a_2T^2[X]+\cdots+a_nT^n[X]=0$. If…