Multilinear Algebra

We are gonna use the dotted line again.

Multilinear Algebra is the math of p-vectors and multivectors. Apparently there is some Grassman Algebra in the mix.

A multivector is an element of the exterior algebra of a vector space. This algebra consists of linear combinations of simple k-vectors.

\nu_1 \wedge ... \wedge \nu_k

where \nu_1, \nu_2, ...,\nu_k are in vector space V.

A multivector is either a k-vector or a linear combination of k-blades.

\nu_1 \wedge nu_2 is a Wedge Product.

  • k=0 \leftrightarrow scalars
  • k=1 \leftrightarrow vectors
  • k=2 \leftrightarrow bivectors
  • k=3 \leftrightarrow trivectors

… … .. .. . .

In multilinear algebra and tensor analysis, covariance and

Contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.