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Determinant = volume using rows.

  1. Jun 6, 2004 #1
    Is one way of looking of the determinant is its the area of the parallelogram formed by the vectors in 2 dimensions, the volume of the parallelpided in 3 dimensions etc. The sign of the determinant tells you something about the relative position of the vectors. This would make the diagonalisation process the transform that turns the parallelogram into a square, and the parallelpiped into a cube.
     
  2. jcsd
  3. Jun 7, 2004 #2

    matt grime

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    Is that a question?

    Let L denote the n'th exterior power of R^n. Any linear map induces a linear transformation on L. This is just a number. That number is the determinant.
     
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