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Eigenvalues and eigenvectors of non-symmetrical tridiagonal matrix

The question is the following: given a matrix $$A=\begin{pmatrix} 1& 2 & & & & \\ 1& 0& 1 & & & \\ & 1& 0& 1 & &\\ & & \ddots & \ddots & \ddots & \\ & & & 1& 0 & 1\\ & & & …
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