Determinant of a matrix

  • #1
does the determinant of square matrix have a physical meaning??
 

Answers and Replies

  • #2
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Yes!! The determinant is the (oriented) volume of the parallelepiped spanned by the vectors of the matrix.
Example, the determinant

[tex]\left|\begin{array}{cc} a & b\\ c & d\end{array}\right|[/tex]

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

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

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