I have a real symmetric matrix H which is in symbolic form, I need a matrix P that can diagonalize H; also P is orthogonal and its columns are the eigenvectors of H.
How can I doing this in mathematica? Below is my sample matrix.
H = {{λ - u, -t, -Δ, 0},
{-t, -λ - u, 0, -Δ},
{-Δ, 0, -λ + u, t},
{0, -Δ, t, λ + u}} // MatrixForm
Eigenvetors
only give the eigenvetors of my matrix. However, they do not form a orthogonal matrix P. @SimonWoods $\endgroup$P = Transpose[Eigenvectors[H]]
as you suggested, a normalization procedure of each column in P should also be done. After that, P will be an orthogonal matrix with its columns are the eigenvectors of H. Am I right? $\endgroup$