Norm of Eigenvectors from Eigenvalues

(*Norm of Eigenvectors from Eigenvalues*)
(*start*)
Clear[nn, t, n, k, M, x];
nn = 12;(*size of matrix*)
t[n_, 1] = 1;
t[1, k_] = 1;
t[n_, k_] :=
  t[n, k] =
   If[n < k,
    If[And[n > 1, k > 1], -Sum[t[k - i, n], {i, 1, n - 1}], 0],
    If[And[n > 1, k > 1], -Sum[t[n - i, k], {i, 1, k - 1}], 0]];

"T is your favourite nn*nn Hermitian matrix"
T = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
HermitianMatrixQ[T]

TableForm[A = Table[Table[T[[n, k]], {k, 1, nn}], {n, 1, nn}]];
lambdaA = N[Eigenvalues[A]];
TableForm[M = Table[Table[T[[n, k]], {k, 1, nn - 1}], {n, 1, nn - 1}]];
lambdaM = N[Eigenvalues[M]];
Quiet[Table[
  N[Product[(lambdaA[[i]] - lambdaM[[k]]), {k, 1, nn - 1}]/
    Product[If[Not[k == i], (lambdaA[[i]] - lambdaA[[k]]), 1], {k, 1,
      nn}]], {i, 1, nn}]]
Table[Norm[N[Eigenvectors[A]][[i]]]^(-2), {i, 1, nn}]
"The values are equal and thereby the left hand side is equal to the \
right hand side in the formula."
(*end*)