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Multilinear map

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In linear algebra, a multilinear map is a mathematical function of several vector variables that is linear in each variable.

Some examples:

  • Inner product (dot product) is a symmetric bilinear function of two vector variables,
  • Determinant is a skew-symmetric multilinear function of the columns (or rows) of a square matrix.

General discussion of where this leads is at multilinear algebra.

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