# Dyadic product
###### tags: `mma` `mma code snippet` `Math` `Mechanics`

<< Notation`;
Symbolize[
ParsedBoxWrapper[
SubscriptBox["x_", "y_"]]]
Symbolize[
ParsedBoxWrapper[
UnderscriptBox["x_", "_"]]]
Notation[ParsedBoxWrapper[
RowBox[{"x_", "\[CircleTimes]", "y_"}]] \[DoubleLongLeftRightArrow] 
  ParsedBoxWrapper[
RowBox[{"DyadicProduct", "[", 
RowBox[{"x_", ",", "y_"}], "]"}]]]
Symbolize[
ParsedBoxWrapper[
SubscriptBox["x_", "1"]]]
Symbolize[
ParsedBoxWrapper[
SubscriptBox["x_", "2"]]]
Symbolize[
ParsedBoxWrapper[
SubscriptBox["x_", "3"]]]

\!\(\*UnderscriptBox[
UnderscriptBox[\(\[CapitalIota]\), \(_\)], \(_\)]\) = {{1, 0, 0}, {0, 
    1, 0}, {0, 0, 1}};
DyadicProduct[x_, y_] :=
 Module[{n = Length[x]},
  Table[x[[i]] y[[j]], {i, 1, n}, {j, 1, n}]]


#### Testing

x = RandomReal[{0, 1}, {3}]
y = RandomReal[{0, 1}, {3}]
(x\[TensorProduct]y) // MatrixForm

$$
\begin{equation}
x=y
\end{equation}
$$

#### TODO Need to look at #jeetika results about NAIR Hybrid III drop test motion reproduction