In mathematics, in particular multilinear algebra, the dyadic product Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... In mathematics, multilinear algebra extends the methods of linear algebra. ...

of a column vector and a row vector is the tensor product of the vectors. The result is a tensor of rank two (a matrix). It is a special case of the tensor product or Kronecker product, for vectors of the same dimension. The word vector means carrier in Latin; it is derived from the Latin verb vehere, which means to carry. ... In mathematics, the tensor product, denoted by , may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras and modules. ... In mathematics, a tensor is a certain kind of geometrical entity, or alternatively generalized quantity. The tensor concept includes the ideas of scalar, vector and linear operator. ... Note: This is a fairly abstract mathematical approach to tensors. ... In mathematics, the tensor product, denoted by , may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras and modules. ... In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. ... Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ...

Example

Definition

Using Einstein's Summation convention, the dyadic product may be defined by . For other topics related to Einstein see Einstein (disambiguation). ... For other topics related to Einstein see Einstein (disambig) In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention useful when dealing with coordinate equations or formulas. ...

Writing out the sums, this becomes .

See also

• Dyadic tensor
• Tensor product