An formula_8 matrix can be seen as describing a linear map in formula_9 dimensions. In which case, the determinant indicates the factor by which this matrix scales (grows or shrinks) a region of formula_9-dimensional space.For example, a formula_11 matrix formula_1, seen as a linear map, will turn a square in 2-dimensional space into a parallelogram. That parallellogram's area will be formula_2 times as big as the square's area.In the same way, a formula_14 matrix formula_15, seen as a linear map, will turn a cube in 3-dimensional space into a parallelepiped. That parallelepiped's volume will be formula_16 times as big as the cube's volume.