Definition:Power (Algebra)/Multiindices

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Definition

Let $k = \left \langle {k_j}\right \rangle_{j = 1, \ldots, n}$ be a multiindex indexed by $\left\{{1, \ldots, n}\right\}$.

Let $x = \left({x_1, \ldots, x_n}\right) \in \R^n$ be an ordered tuple of real numbers.


Then $x^k$ is defined as:

$\displaystyle x^k := \prod_{j \mathop = 1}^n x_j^{k_j}$

where the powers on the right hand side are integer powers.