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dyadic product

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Also 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 sections
Contents
  • 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.

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