I got here in my classical mechanics textbook a set of k equations(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f_{\alpha}(x_1,...,x_N)=0, \ \ \ \ \ \ \alpha=1,...,k[/tex]

and it is said that these k equations are independant when the rank of the matrix

[tex]A_{\alpha i}=\left(\frac{\partial f_{\alpha}}{\partial x_i}\right)[/tex]

is maximal, i.e. equals k.

Could someone explain why this definition makes sense. I.e. why does it meet the intuitive notion of independance, and exactly what this notion of independanceiswhen we're talking about equations. Some references would be nice to!

Thank you all.

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# The notion of independance of equations

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