Eigenvalues of a Special Matrix
- To: mathgroup at smc.vnet.net
- Subject: [mg28006] Eigenvalues of a Special Matrix
- From: Joel Storch <jstorch at earthlink.net>
- Date: Wed, 28 Mar 2001 02:40:34 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Consider the symmetric, Toeplitz matrix A=[a_ij]=cos[(i-j) w]
{i=1,2,...,n ;j=1,2, ....,n}
This matrix has rank 2 and hence at most 2 nonzero eigenvalues.
Generating the eigenvalues for explicit values of n, it is conjectured
that the general expression for the two non-zero eigenvalues are:
lam1=n/2 +1/2 csc w sin(n w) lam2=n/2 ?1/2 csc w
sin(n w)
Can someone produce a formal proof ?