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how to create a symmetric Toeplitz matrix with bounds on eigenvalues?

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Omar B.
Omar B. on 24 Jan 2020
Commented: Christine Tobler on 27 Jan 2020
Is there a way to creat a symmetic Toeplitz matrix of size 400 X 400 with real entries and its largest eigenvalue is 5 and the smallest eigenvalue is -5?
  1 Comment
Matt J
Matt J on 27 Jan 2020
The question as originally posted:
"Is there a way to creat a symmetic Toeplitz matrix of size 400 X 400 with real entries and its largest eigenvalue is 5 and the smallest eigenvalue is -5?"

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Accepted Answer

Matt J
Matt J on 24 Jan 2020
R=fft(eye(400))/sqrt(400);
e=zeros(1,400);
e(2)=-10; e(end-1)=+10;
e=ifftshift(e);
T=(R'*diag(e)*R);
T=real((T+T.')/2);
>> min(eig(T))
ans =
-5.0000
>> max(eig(T))
ans =
5.0000
>> norm(T-T.')
ans =
0

More Answers (1)

Christine Tobler
Christine Tobler on 27 Jan 2020
You can use the MATLAB function toeplitz with one input argument (two-input returns a non-symmetric Toeplitz matrix).
  1 Comment
Christine Tobler
Christine Tobler on 27 Jan 2020
@Matt J, thanks for clarifying. When I was looking at this post 2 hours ago, it was only asking for symmetric Toeplitz matrix, without the condition on the eigenvalues.

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