- Dyadic product
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In mathematics, in particular multilinear algebra, the dyadic productof two vectors, and , each having the same dimension, is the tensor product of the vectors and results in a tensor of order two and rank one. It is also called outer product.
Contents
Components
With respect to a chosen basis , the components Pij of the dyadic product may be defined by
- ,
where
- ,
- ,
and
- .
Matrix representation
The dyadic product can be simply represented as the square matrix obtained by multiplying as a column vector by as a row vector. For example,
where the arrow indicates that this is only one particular representation of the dyadic product, referring to a particular basis. In this representation, the dyadic product is a special case of the Kronecker product.
Identities
The following identities are a direct consequence of the definition of the dyadic product[1]:
See also
Notes
- ^ See Spencer (1992), page 19.
References
- A.J.M. Spencer (1992). Continuum Mechanics. Dover Publications. ISBN 0486435946..
Categories:- Tensors
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