# Eigenvalues and eigenvectors of this matrix

## Main Question or Discussion Point

Consider the nXn matrix A whose elements are given by,

[TEX] A_{ij} = 1 if i=j+1 or i=j-1 or i=1,j=n or i=n,j=1
= 0 otherwise
[/TEX]
What are the eigenvalues and normalized eigenvectors of A??

You could start by calculating the characteristic polynomial. Put $-\lambda$ on the diagonal entries and calculate the determinant. Expanding along the first row or column should be easy, because most entries are zero anyway. You might get a recursive equation ;)