By the way, the determinant of a matrix is just the outermorphism of the associated linear transformation applied to a unit pseudoscalar. The outermorphism of

By the way, the determinant of a matrix is just the outermorphism of the associated linear transformation applied to a unit pseudoscalar. The outermorphism of a linear transformation is a useful and convenient (but sometimes tricky) concept. It gives you not only determinants, but also the application of your linear transformation to arbitrary multivectors.