Eigenvalues and eigenvectors of this matrix

shouvikdatta8
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Consider the nXn matrix A whose elements are given by,

A_{ij} = 1 if i=j+1 or i=j-1 or i=1,j=n or i=n,j=1<br /> = 0 otherwise<br />
What are the eigenvalues and normalized eigenvectors of A??
 
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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 ;)
 

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