Assertion: determinant | /r/HasProperty | negative
Facets:
value: as per the linear mapping preserves
type: OTHER
Source sentences:
text: The determinant is positive or negative according to whether the linear mapping preserves or reverses the orientation of n-space.
text: The determinant is positive or negative according to whether the linear mapping preserves or reverses the orientation of n-space.
text: Yes, it is possible for a determinant to be a negative number.
text: The determinant can be negative.
text: Question 6: Can determinants ever be negative?
text: Question 4: Can a determinant be negative?
text: The determinant can be negative.
text: The determinant is positive or negative as per the linear mapping preserves or changes the orientation of n-space.
text: Determinants are similar to absolute values, and use the same notation, but they are not identical, and one of the differences is that determinants can indeed be negative.
text: either +1 or -1 according to whether the determinant is positive or negative.
text: The determinant can be negative.
text: That's -- now it's -- possible that the determinant is negative.
text: If the determinant is negative, then the volume, we, we should take the absolute value really.
text: More generally, if the determinant of A is positive, A represents an orientation-preserving linear transformation (if A is an orthogonal 2 × 2 or 3 × 3 matrix, this is a rotation), while if it is negative, A switches the orientation of the basis.
text: The determinant is positive or negative as per the linear mapping preserves or changes the orientation of n-space.
text: Its absolute value equals the area (in R2) or volume (in R3) of the image of the unit square (or cube), while its sign corresponds to the orientation of the corresponding linear map: the determinant is positive if and only if the orientation is preserved.
text: The determinant of a set of vectors is positive if the vectors form a right-handed coordinate system, and negative if left-handed.
text: Since the determinant was positive, $T$ preserves the orientation of objects: in both the interval $$ and its image $$, red points are to the right of green points.
text: And the determinant was positive even though it rotated everything so that points on the right are mapped to points on left and points on the top are mapped to points on the bottom.
text: Since the determinant is positive, it preserves the orientation of objects.
text: either +1 or -1 according to whether the determinant is positive or negative.
text: But, a determinant can be a negative number.
text: The determinant can be a negative number.