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