Why are diagonal elements eigenvalues after diagonalizing a matrix

Why are diagonal elements eigenvalues after diagonalizing a matrix

Let p ^ - 1AP = diag (λ 1,..., λ n) P = (α 1,..., α n), then AP = P diag (λ 1,..., λ n), that is, (a α 1,..., a α n) = (λ 1 α 1,..., λ n α n), so there is a α I = λ I α I, I = 1,2,..., N, that is, diagonal elements are eigenvalues, and column vectors of invertible matrix P are corresponding eigenvalues

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