Definition:Multiindex

Definition
Let $J$ be a set.

A multiindex is a sequence:
 * $k = \left \langle {k_j}\right \rangle_{j \in J}$

with only finitely many of the $k_j$ non-zero.

The plural is multiindices (or multi-indices).

Addition
Addition of multiindices is defined as:
 * $\left \langle {k+k'}\right \rangle_j := k_j + k_j'$

Modulus
The modulus of a multiindex $k = \left \langle {k_j}\right \rangle_{j \in J}$ is defined by:
 * $\displaystyle |k| = \sum_{j \in J}k_j$