Does the Determinant of a Square Matrix Have a Physical Meaning?

[Garvit Goel]

does the determinant of square matrix have a physical meaning??

 

[micromass]

Yes! The determinant is the (oriented) volume of the parallelepiped spanned by the vectors of the matrix.
Example, the determinant

$$\left|\begin{array}{cc} a & b\\ c & d\end{array}\right|$$

is the (oriented) area of the parallelogram with vertices (0,0), (a,b), (c,d), (a+c,b+d).

Another application of the determinant is to check whether a certain basis is positive or negative. You just need calculate the determinant of the basis, and depending on whether the answer is positive or negative, the basis has a specified positive/negative orientation.

More information can be found on http://en.wikipedia.org/wiki/Determinant