Newton's identities and matrices

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Newton's identities relate the power sums of the eigenvalues of a matrix to its invariants. The statements that ek equals the kth invariant Ik, pk equals the trace of Ak, and hk equals the determinant of Ak are affirmed as correct. The matrix A is defined as a diagonal matrix with eigenvalues x1, x2, ..., xn. These identities are essential in understanding the relationships between the eigenvalues and the matrix's characteristics. The discussion emphasizes the importance of these identities in matrix theory.
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}##
 

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