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I'm curious as to whether Gauss-Jordan elimination has an equivalent approach for systems of equations involving non-linear terms, for example:

$$ \begin{align} x^3 y^3 z^3 &= 1\\ xy^5 z^3 &= 2\\ xy^3 z^5 &= 3 \end{align} $$

I can solve these equations manually by reducing the terms, but I'm struggling to find a matrix form (does one exist?) to represent it in.

Dmitri Nesteruk
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    Nonlinear is too broad. Polynomial is the keyword. Also, take a look at https://en.wikipedia.org/wiki/Buchberger%27s_algorithm – Rodrigo de Azevedo Sep 20 '16 at 23:59
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    In your particular case, take logarithms on both sides, and you get a linear algebra problem with variables $\log x, \log y, \log z$. – Qiaochu Yuan Sep 21 '16 at 00:04

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