Eigenvalues and eigenvectors of this matrix

shouvikdatta8

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??

CompuChip

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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shouvikdatta8	Eigenvalues and eigenvectors of this matrix Tweet 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??

CompuChip Blog Entries: 5 Recognitions: Homework Help Science Advisor	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 ;)