# ℓ1 Norm Distance Function

(Redirected from L1 Norm Distance Function)

An ℓ1 norm distance function is a Minkowski distance function with $d=1$ (that represents the shortest distance in unit steps along each axis between two points).

## References

### 2009

• (Weisstein, 2009-11-02) ⇒ Eric W. Weisstein. (2009). “L1-Norm." From MathWorld - A Wolfram Web Resource. http://mathworld.wolfram.com/L1-Norm.html
• A vector norm defined for a vector $\mathbf{x}=[x_1, x_2, ..., x_n]$, with complex entries by $|x|_1=\sum_{r=1}^n|x_r|$. The $L^1$-norm $|x|_1$ of a vector $x$ is ...

### 1990

• (Horn & Johnson, 1990) ⇒ R. A. Horn, and C. R. Johnson. (1990). “Norms for Vectors and Matrices." Ch. 5 in Matrix Analysis. Cambridge University Press.