Taxicab Norm is Norm

Theorem

The taxicab norm is a norm on the real and complex numbers.

Proof

By P-Norm is Norm, $\norm {\, \cdot \,}_p$ is a norm.

By definition, the taxicab norm is $\norm {\, \cdot \,}_1$.

Therefore, the taxicab norm is a norm.

$\blacksquare$

Also see

• P-Norm is Norm
• Euclidean Space is Normed Vector Space