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

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?

[Matt J]

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?"

Answer 1

[Matt J]

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

[Omar B.]

Thank you so much. Is it Toeplitz matrix?

[Matt J]

I claim that it is, but it's always smart to check.

Answer 2

[Christine Tobler]

You can use the MATLAB function toeplitz with one input argument (two-input returns a non-symmetric Toeplitz matrix).

[Christine Tobler]

@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.