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From a complete set of orthogonal basis vector ##|i\rangle## ##\in## Hilbert space (##i## = ##1## to ##n##), I construct and obtain a nondiagonal Hamiltonian matrix

$$

\left( \begin{array}{cccccc}

\langle1|H|1\rangle & \langle1|H|2\rangle & . &. &.& \langle1|H|n\rangle \\

\langle2|H|1\rangle & . & . &. &.&. \\

. & . & . &. &.&. \\

. & . & . &. &.&. \\

. & . & . &. &.&. \\

. & . &. &. &.& \langle n|H|n\rangle \end{array} \right)

$$

After diagonalization, I obtain diagonal ##n\times n## matrix that represent the eigenvalues of the Hamiltonian, and another ##n\times n## matrix ##V## composed of scalars that represent the eigenvectors of the same Hamiltonian.

My question is, what is the link between the scalar matrix ##V## and the complete set of orthogonal basis vector ##|i\rangle## that I choose in the beginning ?

Thank you very much everybody.

Konte