Whenever this happens, whenever the orientation of space is inverted, the determinant will be negative.

每当这种情况发生 每当空间的方向是颠倒的 行列式就是负的。

Any transformations that do this are said to invert the orientation of space.

任何这样的变换都被称为颠倒空间的方向。

If after a transformation, j hat is now on the right of I hat, the orientation of space has been inverted.

如果经过一个变换 j帽现在在I帽的右边 空间的方向就颠倒了。