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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Encyclopedic overview
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.
Excerpted from Wikipedia’s “dyadic product” article, available under the CC BY-SA 4.0 licence.