001多重线性函数

$$p个m维向量u_1\dots \dots u_p$$
$$\varphi (u_1\dots \dots u_p)\in R$$
$$对每个u_i线性:\varphi (u_1\dots a{\bar{u}}_i+b{\hat{u}}_i\dots u_p)=a\varphi (u_1\dots {\bar{u}}_i\dots u_p)+b\varphi (u_1\dots {\hat{u}}_i\dots u_p)$$
$$\begin{gathered} 以上记为p阶张量集合：{\mathcal{T}}^p(R^m) \\ 给其赋予线性结构 \end{gathered}$$
$$(a\varphi +b\psi )(u_1\dots \dots u_p)定义为a\varphi (u_1\dots \dots u_p)+b\psi (u_1\dots \dots u_p)\in R$$