Dyadic Product

A Dyadic is a second order Tensor.

The Dyadic Product takes two Vectors and returns a Dyadic.

\begin{bmatrix}a_x \\a_y \\a_z \end{bmatrix} \otimes \begin{bmatrix} b_x \\b_y \\b_z \end{bmatrix} = \begin{bmatrix} a_xb_x & a_xb_y & a_xb_z \\a_yb_x & a_yb_y & a_yb_z \\a_zb_x & a_zb_y & a_zb_z \end{bmatrix}

When we see this example, we see that it is the same thing that was also called the Outer Product.

The Dyadic Product of two vectors, a and b, is denoted by ab, without any further decoration.

We found this: “the formalism of Dyadic Algebra is an extension of Vector Algebra to include the Dyadic Product of Vectors.”

And then we found this: “Dirac’s bra-ket notation makes the use of dyads and dyadics intuitively clear.” Well, that’s an awfully big promise, but hopefully there lies some truth in it.”

Oh, and two vectors multiplied with that symbol that is a circle with an x in it, form a Tensor Product (and we know that already has another name).