I have some difficulties picturing why "orientation" is related to determinant of matrix.
In fact I find it hard to visualize exactly what "orientation" is.
Arthas007
determinant in linear algebra is very complex. So much abstraction between space and number
hlin1
This seems to imply that reflecting on two axis will result in no change in orientation, is that correct?
Max
@whc if you think about the determinant of a matrix as representing the volume scaling factor of the transformation it represents, you might be able to see that flipping the sign is like inverting the volume, which is reversing orientation.
@hlin1 right - what matters is the parity of the number of reflections you do. 1 -> flip, 2-> no flip, 3 -> flip, etc.
I have some difficulties picturing why "orientation" is related to determinant of matrix.
In fact I find it hard to visualize exactly what "orientation" is.
determinant in linear algebra is very complex. So much abstraction between space and number
This seems to imply that reflecting on two axis will result in no change in orientation, is that correct?
@whc if you think about the determinant of a matrix as representing the volume scaling factor of the transformation it represents, you might be able to see that flipping the sign is like inverting the volume, which is reversing orientation.
@hlin1 right - what matters is the parity of the number of reflections you do. 1 -> flip, 2-> no flip, 3 -> flip, etc.