# 外积

## 矩阵乘法定义

$\mathbf{u} \otimes \mathbf{v} = \mathbf{A} = \mathbf{u} \mathbf{v}$

$\begin{bmatrix}b_1 \\ b_2 \\ b_3 \\ b_4\end{bmatrix} \otimes \begin{bmatrix}a_1 & a_2 & a_3\end{bmatrix} = \begin{bmatrix}a_1b_1 & a_2b_1 & a_3b_1 \\ a_1b_2 & a_2b_2 & a_3b_2 \\ a_1b_3 & a_2b_3 & a_3b_3 \\ a_1b_4 & a_2b_4 & a_3b_4\end{bmatrix}$

$\mathbf{u} \otimes \mathbf{v} = \mathbf{A} = \mathbf{u} \bar{\mathbf{v}}$

$\mathbf{u} \otimes \mathbf{v} = \mathbf{A} = \mathbf{u} \mathbf{v}^*$

### 相对于内积

$\left\langle \mathbf{u}, \mathbf{v}\right\rangle = \left\langle \mathbf{v}, \mathbf{u}\right\rangle = \mathbf{v} \mathbf{u}$

## 抽象定义

$A(w) := w^*(w)v$
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