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quasar987

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## Main Question or Discussion Point

I got here in my classical mechanics textbook a set of k equations

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

and it is said that these k equations are

[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 independance

Thank you all.

[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 independance

*is*when we're talking about equations. Some references would be nice to!Thank you all.