A linear map sends a unit square to the parallelogram spanned by its column vectors. The determinant measures oriented area: its magnitude is the area scale and its sign records whether orientation is reversed.线性映射将单位正方形变为由矩阵列向量张成的平行四边形。行列式度量有向面积：绝对值是面积缩放倍数，符号表示方向是否翻转。
The grid deforms continuously from the identity to . At the endpoint, the highlighted square has area 1.19.网格从恒等变换连续形变到 。在终点，高亮正方形的像面积为 1.19。