Newton's identities and matrices

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Jhenrique
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About the Newton's identities:
Newton_s_identities.png


I'm right if I state that ek = Ik, pk = tr(Ak) and hk = det(Ak) (being Ik the kth-invariant of the matrix A)?
 
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PS: being ##A = \begin{bmatrix}
x_1 & 0 & \cdots & 0 \\
0 & x_2 & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & x_n \\
\end{bmatrix}##