Physical interpretation of a determinate?

In summary, the determinant is a function that maps a square matrix to an element of a field. It can have different interpretations, such as determining the volume of a prism, but there is no one specific physical interpretation for it. It is often used in calculating tensor densities.
  • #1
Xyius
508
4
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?

Thanks!
~Matt
 
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  • #2


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.
 
  • #3
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".
 

1. What is a determinate?

A determinate is a physical quantity or property that can be measured or calculated with certainty. It has a specific value and does not vary or change.

2. How is a determinate different from an indeterminate?

A determinate has a specific value and is known with certainty, while an indeterminate has a range of possible values and is not known with certainty.

3. Can determinates be observed directly?

No, determinates are abstract concepts that cannot be observed directly. They can only be measured or calculated based on observable phenomena.

4. What is the significance of understanding the physical interpretation of a determinate?

Understanding the physical interpretation of a determinate allows scientists to accurately measure and describe the physical world. It also helps in making predictions and developing theories to explain natural phenomena.

5. How are determinates used in scientific experiments?

Determinates are used in scientific experiments as variables that can be controlled and measured to test hypotheses and gather data. They are essential in the scientific method and in establishing cause-and-effect relationships.

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