## Newton tensor

Suppose is a symmetric endomorphism of vector space , is the th elementary symmetric function of the eigenvalue of . Then

One can define the th Newton transformation as the following

This means

By comparing coefficients of , we get the relations of

Induction shows

For example

One of the important property of Newton transformation is that: Suppose , then

The is because

If , then is positive definite and therefore is elliptic.

**Remark:** Hu, Z., Li, H. and Simon, U. . Schouten curvature functions on locally conformally flat Riemannian manifolds. Journal of Geometry, 88(12), (2008), 75100.

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## Comments

I mean practical. Like for a diagonal matrix. Is the Newton tensor a matrix?