tensor 積
tensor product
可換圖式$ V\times W\xrightarrow{\otimes}V\otimes W\xrightarrow{\exist!\tilde h}Z\xleftarrow{h}V\times W code:tex
A\otimes B=
\begin{pmatrix}
a_{11} & \cdots & a_{1n} \\
\vdots & \ddots & \vdots \\
a_{m1} & \cdots & a_{mn}
\end{pmatrix}\otimes
\begin{pmatrix}
b_{11} & \cdots & b_{1q} \\
\vdots & \ddots & \vdots \\
b_{p1} & \cdots & b_{pq}
\end{pmatrix} :=
\begin{pmatrix}
a_{11}b_{11} & \cdots & a_{11}b_{1q} & \cdots & a_{1n}b_{11} & \cdots & a_{1n}b_{1q} \\
\vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\
a_{11}b_{p1} & \cdots & a_{11}b_{pq} & \cdots & a_{1n}b_{p1} & \cdots & a_{1n}b_{pq} \\
\vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\
a_{m1}b_{11} & \cdots & a_{m1}b_{1q} & \cdots & a_{mn}b_{11} & \cdots & a_{mn}b_{1q} \\
\vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\
a_{m1}b_{p1} & \cdots & a_{m1}b_{pq} & \cdots & a_{mn}b_{p1} & \cdots & a_{mn}b_{pq} \\
\end{pmatrix}
tensor 代數
tensor 空閒