How do I reduce a symmetric matrix to a tridiagonal matrix with the same eigenvalues?

Question

I have a symmetric matrix found from the following commands:

a=rand(n);
A=triu(a)+triu(a,1)'

I was wondering how I reduce this symmetric matrix into a tridiagonal matrix?

Any help is appreciated. Thank you very much.

Answer 1

What you want is to find the upper Hessenberg form of your matrix. For a symmetric matrix, this is tridiagonal.

Use the command hess to do this:

B=hess(A);