Dyadic tensor
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A dyadic tensor in multilinear algebra 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° rotation operator in two dimensions. It can be dotted (from the left) with a vector to produce the rotation:
