You can use the eig function to calculate the eigen value and corresponding eigen vector of a matrix
A = [1 2 0; 2 5 -1; 4 10 -1]
[V,D] = eig(A)
returns diagonal matrix D of eigenvalues and matrix V whose columns are the corresponding right eigenvectors, so that A*V = V*D.
You can refer to following documentation to know more about the implementation of eig() function
To know more about Hamiltonian matrix and its matrix method calculation you can refer to the following link.
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