Outer Product

The outer product of two coordinate vectors is a matrix. A coordinate vector is an ordered list of numbers that describes the vector in terms of a particular ordered basis.

Outer Product appears to be synonymous with Dyadic Product. We say “appears to be” because sometimes one thing is a generalization of the other, and at low levels (such as three dimensions or lower) they are identical.

The calculation for an Outer Product is shown below:

u \otimes v = \begin{bmatrix}u_1 \\u_2 \\u_3 \end{bmatrix}\begin{bmatrix}\overline{v_1} & \overline{v_2} & \overline{v_3}\end{bmatrix} = \begin{bmatrix}u_1\overline{v_1} & u_1\overline{v_2} & u_1\overline{v_3} \\ u_2\overline{v_1} &  u_2\overline{v_2} & u_2\overline{v_3} \\ u_3\overline{v_1} &  u_3\overline{v_2} & u_3\overline{v_3}\end{bmatrix}

The Outer Product is used twice in the calculation of the Wedge Product.

— — —

Internal question: does the word “coordinate” impart anything substantial to “vector”? Or is it redundant like saying a warm mammal?