I agree, the way I still see determinant is as the 'volume scaling factor' of a linear transformation.
This means it makes sense that det(A) = 0 means A is non-invertible. It also makes a lot of sense when the jacobian pops up in the multi-dimensional chain rule.
Given the above, and the Cayley–Hamilton theorem, I never really had to know why the determinant was calculated the way it is. The above give enough of an interface to work with it.
This means it makes sense that det(A) = 0 means A is non-invertible. It also makes a lot of sense when the jacobian pops up in the multi-dimensional chain rule.
Given the above, and the Cayley–Hamilton theorem, I never really had to know why the determinant was calculated the way it is. The above give enough of an interface to work with it.