Let V1,V2,,Vn,W be vector spacesMathworldPlanetmath over a field K. A mapping


is called multi-linear or n-linear, if M is linear in each of its arguments.


  • A bilinear mapping is another name for a 2-linear mapping.

  • This definition generalizes in an obvious way to rings and modules.

  • An excellent example of a multi-linear map is the determinantDlmfMathworldPlanetmath operation.

Title multi-linear
Canonical name Multilinear
Date of creation 2013-03-22 12:33:05
Last modified on 2013-03-22 12:33:05
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 10
Author rmilson (146)
Entry type Definition
Classification msc 15A69
Synonym multi-linearity
Synonym multilinear
Synonym multilinearity
Related topic BilinearForm
Related topic BilinearMap