Dyadic tensor
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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:

$(\backslash \backslash mathbf\{j\; i\}\; -\; \backslash \backslash mathbf\{i\; j\})\; \backslash \backslash cdot\; (x\; \backslash \backslash mathbf\{i\}\; +\; y\; \backslash \backslash mathbf\{j\})\; =$

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}.

The original article can be found at: http://en.wikipedia.org/wiki/Dyadic_tensor.
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