Dyadic tensor
A dyadic tensor is a second rank tensor written in a special notation, formed by juxtaposing pairs of vectors, i.e. placing pairs of vectors side by side.
Each component of a dyadic tensor is a dyad. A dyad is the juxtaposition of a pair of basis vectors and a scalar coefficient.
As an example, let and be a pair of two-dimensional vectors. Then the juxtaposition of A and X is
- .
The identity dyadic tensor in three dimensions is i i + j j + k k. The dyadic tensor j i - i j is a 90 degree rotation operator in two dimensions. It can be dotted (from the left) with a vector to produce the rotation:
x \\mathbf{j i} \\cdot \\mathbf{i} - x \\mathbf{i j} \\cdot \\mathbf{i} + y \\mathbf{j i} \\cdot \\mathbf{j} - y \\mathbf{i j} \\cdot \\mathbf{j} =
-y \\mathbf{i} + x \\mathbf{j}.
