Assertion: matrix's value | /r/CapableOf | equal volume
Facets:
value: in r
type: LOCATION
value: in r3
type: LOCATION
Source sentences:
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: Its absolute value equals the area (in R 2 {\displaystyle \mathbb {R} ^{2}} ) or volume (in R 3 {\displaystyle \mathbb {R} ^{3}} ) 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.