Vectors, tensors, and dyadics

A vector in three-dimensional Cartesian space is characterized by three components 

Because of the orthogonality of the unit vectors in a scalar or dot product, the scalar product of two vectors A and B can be expressed as 

A dot product of two vectors yields a single number, a scalar. It is possible to generate a three-by-three matrix by the multiplication of two vectors. This 

The result of this operation is called a dyadic or tensor 

A dyadic behaves like a two-headed vector -- the scalar product of D with a vector A yields a vector 

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