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I want to generate a (large) matrix with eigenvalues that are all in a small interval. The relationship between the maximum eigenvalue and minimum eigenvalue should be as small as possible, that's the goal. And the eigenvalues must all be positive.

Is there any simple way to do this? I'm using Mathcad, and I've built a function to randomly generate a symmetric matrix. And when I want all the eigenvalues positive, I just use the matrix multiplied by it's transpose. But the eigenvalues are scattered in a large interval, and the relationship between the max eigenvalue and min eigenvalue is in the hundreds and thousands. Any tricks to make the eigenvalues get closer to each other?

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# Creating a matrix with desirable eigenvalues

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