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# Determinant of matrices watch

1. I've finished the matrices chapter in P6 ... but it seems not enough about matrices.

As I know determinant of square matrix (n x n),A is
|A| = Sum[j:1->n] of Aij.Mij (i is any value from 1-n)
where Aij = (-1)^(i+j).aij (aij is the term in matrix A)
and Mij is the square matrix of size of (n-1), cross out ith row and jth column.
(In the book, there are only (2x2) and(3x3) matrices.)

But I wonder if the matrix is not square (m x n) where m <> n, will it have determinant or not?
2. I'm pretty sure only square matrices have determinants because a square matrix represents a transformation and the determinant is the area scale factor of the unit square under the transformation. A non square matrix can't transform a vector to another vector of the same dimensions.
3. Thanks

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Updated: February 4, 2005
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