Math

符号 {symbols}

for	sym	html	latex	cn
plus		+	$+$
minus		−	$-$
Multiplication		×	$\times$
Division		÷	$\div$
Not Equal To		≠	$\ne$
Plus minus		±	$\plusmn$
real number	ℝ	ℝ	$\mathbb R$	实数
sum	∑	∑	$\sum$	求和
Delta	Δ	Δ	$\Delta$
Nabla	∇	∇	$\nabla$	纳布拉
ceiling	⌈⌉	⌈⌉	$\lceil \rceil$
floor	⌊⌋	⌊⌋	$\lfloor \rfloor$
Angle Bracket	⟨ ⟩	⟨ ⟩	$\lang \rang$
Dot Operator	⋅	⋅	$\sdot$
verbar		\|	$\vert$

note

vector: an element of a vector space; $\reals ^n$; Euclidean vector; Hilbert space
Length: 长度

\begin{alignat*}{2} \left\|\mathbf{a}\right\| &= \sqrt{\mathbf{a}\cdot\mathbf{a}} \\ &= \sqrt{a_1^2+a_2^2+a_3^2} \\ &= \sqrt{\sum_{i=1}^n a_i^2} \end{alignat*}

Dot product: 标量积; 点积; $\mathbf{a}\cdot\mathbf{b}=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\cos\theta$; $\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3$; $\left(x_1,\:\:\ldots ,\:\:x_n\right)\cdot \left(b,\:\:\ldots ,\:\:y_n\right)=\sum _{i=1}^nx_iy_i$
Cross product: 矢量积; $\mathbf{a}\times\mathbf{b}=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\sin(\theta)\,\mathbf{n}$

矩阵

张量

rank 0 - scalar - 标量、纯量
rank 1 - vector - 向量
rank 2 - matrix - 矩阵
rank $m$ $m$ - $d_1 \times d_2 \times \cdots \times d_m$ $d_{1} \times d_{2} \times \dots \times d_{m}$ where $d_i > 0$ $d_{i} > 0$
- $m$ - 称作秩或阶
协变张量 - 指标在下
逆变张量 - 指标在上
混合张量 - 上下都有指标