Origin¶

Definition¶

The origin of $\mathbb{R}^n$ is the vector whose coordinates are all zero:

Interpretation¶

The origin is the point of $\mathbb{R}^n$ with all coordinates equal to zero, the point where the coordinate axes cross. As a vector, it is the zero vector of the real coordinate space $\mathbb{R}^n$: adding it to any vector changes nothing.

As a point, the origin is the reference point of the Cartesian coordinate system: the coordinates of any other point say how far, and in which direction, it lies from the origin along each axis. Position vectors are drawn as arrows starting there. Every subspace of $\mathbb{R}^n$ contains the origin, so lines and planes that miss it are not subspaces.

Key Results¶

• Position vectors are often drawn as arrows starting at the origin.

Examples¶

• In $\mathbb{R}^2$, the origin is $(0,0)$.

Prerequisites¶

• Zero Vector
• Coordinate

Related Concepts¶

• Euclidean Space
• Cartesian Coordinate System
• Vector

Sources¶

• Math II: Linear Algebra · Week 2

Aliases: zero point, coordinate origin Symbols: real numbers

Last updated: 20 October 2026 03:02