dyadic product
Sign in to saveAlso known as dyadic tensor, tensor product, tensor product of vectors, tensor product of two vectors
In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra.
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Article
27 sectionsContents
- Definitions and terminology
- Dyadic, outer, and tensor products
- Three-dimensional Euclidean space
- ''N''-dimensional Euclidean space
- Classification
- Identities
- Dyadic algebra
- Product of dyadic and vector
- Product of dyadic and dyadic
- Double''–''dot product
- Double''–''cross product
- Tensor contraction
- Unit dyadic
- Properties of unit dyadics
- Examples
- Vector projection and rejection
- Rotation dyadic
- 2d rotations
- 3d rotations
- Lorentz transformation
- Related terms
- See also
- Notes
- Explanatory notes
- Citations
- References
- External links
In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra.
There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product returns a pseudovector. Both of these have various significant geometric interpretations and are widely used in mathematics, physics, and engineering. The dyadic product takes in two vectors and returns a second order tensor called a dyadic in this context. A dyadic can be used to contain physical or geometric information, although in general there is no direct way of geometrically interpreting it.