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Physical interpretation of a determinate?

  1. Jun 25, 2010 #1
    I just finished my first Linear Algebra class and loved it. There is one thing we didn't go over much though. What exactly IS a determinate? Is there a physical interpretation? Or is it just an operator that has these special properties?

  2. jcsd
  3. Jun 25, 2010 #2


    Staff: Mentor

    Re: Physical interpretation of a determinANT?

    You mean determinant. There are many kinds of determinant, one for 2 X 2 matrices, one for 3 x 3 matrices, and so on. You can think of a determinant as a function that maps a square matrix of a particular size to an element of some field (e.g., the reals or the complex numbers).

    AFAIK, there isn't any physical interpretation of a determinant.
  4. Jun 26, 2010 #3


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    Science Advisor

    No mathematical concept has one "physical interpretation" but can be given many physical interpretations by applying them to different physical situations.

    One physical interpretation of the determinant is this: if a "prism" (a solid like a "tilted" rectangular solid) has edges at one point given by [itex]a\vec{i}+ b\vec{j}+ c\vec{k}[/itex], [itex]d\vec{i}+ e\vec{j}+ f\vec{k}[/itex], and [itex]g\vec{i}+ h\vec{j}+ i\vec{k}[/itex] then its volume is the determinant
    [tex]\left|\begin{array}{ccc}a & b & c \\ d & e & f\\ g & h & i\end{array}\right|[/tex]

    That, or variations on it, often show up in calculating "tensor densities".
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