Then the dyadic product of a and b can be represented as a sum:

This notation can be confused with the dyadic product between two vectors.

Here, uv is the dyadic product of two vectors u and v.

The products between the two orthogonal unit vectors are dyadic products.

As an example, a very particular linear operator L might be written as a dyadic product:

As there are no analogous matrix operations for the remaining dyadic products, no ambiguities in their definitions appear.

A dyadic product is the special case of the tensor product between two vectors of the same dimension.

The second equation includes the divergence of a dyadic product, and may be clearer in subscript notation:

The following identities are a direct consequence of the definition of the dyadic product, and the linearity of vectors:

The tensor derivative of a vector field is a 9-term second-rank tensor, but can be denoted simply as , where represents the dyadic product.

The divergence of a second-order tensor field in cylindrical polar coordinates can be obtained from the expression for the gradient by collecting terms where the scalar product of the two outer vectors in the dyadic products is nonzero.

A dyad is a tensor of order two and rank one, and is the result of the dyadic product of two vectors (complex vectors in general), whereas a dyadic is a general tensor of order two.

In mathematics, in particular linear algebra, the matrix determinant lemma computes the determinant of the sum of an invertible matrix A and the dyadic product, u v, of a column vector u and a row vector v.