在几何中，以一般化的观点来说，标量是零维的几何量，矢量是一维的有向几何量，依此类推，我们可以有二维的有向几何量。几何代数中的外代数（exterior algebra）采用了这个一般化的观点定义了二重矢量（bivector）。一个二重矢量亦即二维的有向几何量，它是一个有向面积。

二重矢量是使用外积（exterior product）来产生的：令 a 与 b 为矢量，它们的外积 a ∧ b 即为一个二重矢量，代表由 a 与 b 围成的平行四边形面积，其方向为 a 到 b 的时针方向。所以，外积是反对称的，a ∧ b 的方向恰与 b ∧ a 相反。另外，a ∧ a 是一个「零二重矢量」。

In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered an order zero quantity, and a vector is an order one quantity, then a bivector can be thought of as being of order two. Bivectors have applications in many areas of mathematics and physics. They are related to complex numbers in two dimensions and to both pseudovectors and quaternions in three dimensions. They can be used to generate rotations in any dimension, and are a useful tool for classifying such rotations. They also are used in physics, tying together a number of otherwise unrelated quantities.