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Outer product

A matrix with every possible product of elements from two vectors,

\[\begin{equation*}
  \vec{u} \otimes \vec{v}
  = \vec{u} \, \vec{v}^\mathsf{T}
  =
  \begin{pmatrix} u_1 \\ \vdots \\ u_m \end{pmatrix}
  \begin{pmatrix} v_1 & \cdots & v_n \end{pmatrix}
  =
  \begin{pmatrix}
    u_1 v_1 & \cdots & u_1 v_n \\
    \vdots & \ddots & \vdots \\
    u_m v_1 & \cdots & u_m v_n
  \end{pmatrix}.
\end{equation*}
\]

• Synonyms
• Computing tools
• Dimensionality: Vectors
• Dimensionality: Tensors