3 ms·
Determinants aren't inherently abstract, they're quite practical, especially in the article's context: they tell you the scaling factor of the transformation th
by mkl 6y ago
Determinants aren't inherently abstract, they're quite practical, especially in the article's context: they tell you the scaling factor of the transformation the matrix represents, and whether it does a reflection.
E.g. the determinants of the rotation matrices in the article are all 1, because they don't scale or reflect anything, just rotate.
- MiroF 6y agoThe matrix {{1,0,0},{0,-1,0},{0,0,-1}} has a determinant of 1 too, but it reflects along two different axes. So there's no way to distinguish from the determinant between the identity and between a reflection across two axes. I think the important detail is if you're changing from right-handed bases to left-handed or vice versa during the transformation.
- rumanator 6y ago> So there's no way to distinguish from the determinant between the identity and between a reflection across two axes. I fail to see the point you tried to make. Both transformations preserve volume. Why did you expected volume to change if you rotate something?
- MiroF 6y agoParent comment claims you can use determinant to see if a reflection is occurring, I disagreed. I don't know where you thought I expected volume to change if I rotate something.
- mkl 6y agoTwo reflections make a rotation. Your matrix is a rotation matrix that does no reflection (everything will be oriented the same way after being transformed).
- MiroF 6y agoYou're right, cheers.