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For equation $y = x*z$, assuming $x$, $y$, and $z$ are unknown, what is the correct terminology for describing it?

I'm assuming it is not quadratic since there is no squared term (e.g., $x^2$) and not linear since $x$ and $z$ are both unknowns (unless "linearity" is always with respect to a particular variable?), so maybe "non-linear equation" is the best fit?

Dolan Antenucci
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  • Just noticed this related post that refers to it as "bilinear": https://math.stackexchange.com/questions/728829/terminology-of-linear-quadratic-etc-for-multi-input-functions?rq=1 – Dolan Antenucci Dec 30 '17 at 18:46

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Are you sure you want a name for this? With the same justification you could call the equation "nonlogarithmic".

If it is really important you could explicitly remark that

"The variables $x$, $y$, $z$ are not linearly related."

Here "linearly related" means that there are constants $a$, $b$, $c$, $d$, not all of them $=0$, such that $$ax+by+cz=d\ .$$

Christian Blatter
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  • Thanks. You make a good point regarding alternative names. My reasoning is I have a constrained-optimization problem I'm solving with a 3rd party solver (AMPL), and one of my constraints is of this format, so I wanted to be clear in my description of it. I think something along the lines of your suggestion will work – Dolan Antenucci Dec 30 '17 at 18:37