In somewhere in wikipedia, I found a "shortcut" for compute the jacobian, the formula is: [tex]\frac{\partial(q_1 , q_2 , q_3)}{\partial (x, y, z)} = h_1 h_2 h_3[/tex] where q represents the coordinate of other system and h its factor of scale.(adsbygoogle = window.adsbygoogle || []).push({});

I know that this relationship is true. What I'd like of know is if this equation below is true: [tex]\frac{\partial(q_1 , q_2 , q_3)}{\partial (Q_1, Q_2, Q_3)} = \frac{h_1 h_2 h_3}{H_1 H_2 H_3}[/tex] where Q represents the coordinate ofanothersystem and H its factor of scale.

Is correct to affirm that the jacobian is equal to the quotient between the scale factors?

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# Shortcut to jacobian

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