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An alternating multilinear map is a special type of multilinear function that takes several input arguments from a vector space and has the property of being alternating. Here's a more detailed breakdown of what this means: 1. **Multilinear Map**: A function \( f: V_1 \times V_2 \times \ldots \times V_n \to W \) is called multilinear if it is linear in each of its \( n \) arguments.