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Eigenvalues and eigenvectors of this matrix

  1. Aug 18, 2009 #1
    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
    What are the eigenvalues and normalized eigenvectors of A??
  2. jcsd
  3. Aug 18, 2009 #2


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    You could start by calculating the characteristic polynomial. Put [itex]-\lambda[/itex] 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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