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Shortcut to jacobian

  1. Feb 26, 2014 #1
    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.

    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 of another system and H its factor of scale.

    Is correct to affirm that the jacobian is equal to the quotient between the scale factors?
     
  2. jcsd
  3. Mar 11, 2014 #2
    What you did is to invent a definition of [tex]\frac{\partial(q_1 , q_2 , q_3)}{\partial (Q_1, Q_2, Q_3)} .[/tex] It is not true nor false: it is a definition.
     
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