I have a matrix of the following type;

matrix = SparseArray[{{i_, i_} -> Eo, {i_, j_} /; Abs[i - j] == 1 -> -t, {i_, j_} /; i == 1 && j == NA -> -t, {i_, j_} /; j == 1 && i == NA -> -t}, {NA, NA}]; MatrixForm[matrix];

, where the eigenvectors of this matrix is equal to ϕm. I want to show that these coefficients ϕm are wavelike and therefore have been told to take a Fourier Transform of the individual eigenvectors to find it's corresponding frequency peak.

I have tried to make a table and list of the eigenfunctions and then take a Fourier Transform, but it doesn't seem to be working.

Does anyone have any ideas? Thanks so much in advance!

I have a matrix that looks like this

matrix = SparseArray[
             {{i_, i_} -> Eo, {i_, j_} /;
               Abs[i - j] == 1 -> -t, {i_, j_} /; 
               i == 1 && j == NA -> -t, {i_, j_} /; 
               j == 1 && i == NA -> -t}, {NA, NA}];

MatrixForm[matrix];

where the eigenvectors of this matrix are equal to ϕm. I want to show that these coefficients ϕm are wave-like and therefore have been told to take the Fourier Transform of the individual eigenvectors to find it's corresponding frequency peak.

I have tried to make a table and list of the eigenfunctions and then take a Fourier Transform, but it doesn't seem to be working.

Does anyone have any ideas?