常用数学符号表示 郝伟 2021/0/0 [TOC]
1. 简介
2. 1 数值与数组 Numbers & Arrays
| ID | Notion | Description | 解释 |
|---|---|---|---|
| 1.1 | $a$ | A scalar (integer or ral) | 标量 |
| 1.2 | $\text{A}$ | A scalar constant | 标量常数 |
| 1.3 | $\boldsymbol{a}$ | A vector | 矢量 |
| 1.4 | $\boldsymbol{A}$ | A matrix | 矩阵 |
| 1.5 | $\texttt{A}$ | A tensor | 张量 |
| 1.6 | $\boldsymbol{I}_n$ | The $n\times n$ identity matrix | n阶单位矩阵 |
| 1.7 | $\boldsymbol{D}$ | A diagnonal matrix | 对角矩阵 |
| 1.8 | $\text{diag}(\boldsymbol{a})$ | A square, diagonal matrix with diagonal entries given by $\boldsymbol{a}$ | 由矢量 $\boldsymbol{a}$ 给出的具有对角元素的方形对角矩阵 |
| 1.9 | $\text{a}$ | A scalar random varaiable | 随机标量变量 |
| 1.10 | $\textbf{a}$ | A vector-valued random varaiable | 随机矢量变量 |
| 1.11 | $\textbf{A}$ | A matrix-valued random variable | 随机矩阵变量 |
3. Math Fonts
Ref: Math Font Selection in LaTeX and Unicode, http://milde.users.sourceforge.net/LUCR/Math/math-font-selection.xhtml Mathematical fonts, https://www.overleaf.com/learn/latex/Mathematical_fonts
1. \mathnormal default1
2. \mathrm roman2
3. \mathbf bold roman
4. \mathsf sans serif
5. \mathit text italic
6. \mathtt typewriter
7. \mathcal calligraphic
8. \mathscr 艺术体
9. \mathbb 集合体
\mathnormalis used by default for alphanumeric characters in math mode. It sets the letter shape according to character class and math style. (Table 1 shows the default letter shapes for common math styles).
2.The specifier “roman” is ambiguous: roman shape stands for upright, while roman type stands for serif (as opposed to sans serif).
3.1. Naming scheme
The naming scheme is an extension of the predefined math alphabet commands with the established short-cuts:
bf bold
it italic
cal script (calligraphic)
frak fraktur
bb double-struck (blackboard bold)
sf sans serif
3.2. Samples
| ID | 1.mathnormal | 2.mathrm | 3.mathbf | 4.mathsf | 5.mathit | 6.mathtt | 7.mathcal | 8.mathscr | 9.mathbb |
|---|---|---|---|---|---|---|---|---|---|
| 1 | $\mathnormal{A}$ | $\mathrm{A}$ | $\mathbf{A}$ | $\mathsf{A}$ | $\mathit{A}$ | $\mathtt{A}$ | $\mathcal{A}$ | $\mathscr{A}$ | $\mathbb{A}$ |
| 2 | $\mathnormal{B}$ | $\mathrm{B}$ | $\mathbf{B}$ | $\mathsf{B}$ | $\mathit{B}$ | $\mathtt{B}$ | $\mathcal{B}$ | $\mathscr{B}$ | $\mathbb{B}$ |
| 3 | $\mathnormal{C}$ | $\mathrm{C}$ | $\mathbf{C}$ | $\mathsf{C}$ | $\mathit{C}$ | $\mathtt{C}$ | $\mathcal{C}$ | $\mathscr{C}$ | $\mathbb{C}$ |
| 4 | $\mathnormal{D}$ | $\mathrm{D}$ | $\mathbf{D}$ | $\mathsf{D}$ | $\mathit{D}$ | $\mathtt{D}$ | $\mathcal{D}$ | $\mathscr{D}$ | $\mathbb{D}$ |
| 5 | $\mathnormal{E}$ | $\mathrm{E}$ | $\mathbf{E}$ | $\mathsf{E}$ | $\mathit{E}$ | $\mathtt{E}$ | $\mathcal{E}$ | $\mathscr{E}$ | $\mathbb{E}$ |
| 6 | $\mathnormal{F}$ | $\mathrm{F}$ | $\mathbf{F}$ | $\mathsf{F}$ | $\mathit{F}$ | $\mathtt{F}$ | $\mathcal{F}$ | $\mathscr{F}$ | $\mathbb{F}$ |
| 7 | $\mathnormal{G}$ | $\mathrm{G}$ | $\mathbf{G}$ | $\mathsf{G}$ | $\mathit{G}$ | $\mathtt{G}$ | $\mathcal{G}$ | $\mathscr{G}$ | $\mathbb{G}$ |
| 8 | $\mathnormal{H}$ | $\mathrm{H}$ | $\mathbf{H}$ | $\mathsf{H}$ | $\mathit{H}$ | $\mathtt{H}$ | $\mathcal{H}$ | $\mathscr{H}$ | $\mathbb{H}$ |
| 9 | $\mathnormal{I}$ | $\mathrm{I}$ | $\mathbf{I}$ | $\mathsf{I}$ | $\mathit{I}$ | $\mathtt{I}$ | $\mathcal{I}$ | $\mathscr{I}$ | $\mathbb{I}$ |
| 10 | $\mathnormal{J}$ | $\mathrm{J}$ | $\mathbf{J}$ | $\mathsf{J}$ | $\mathit{J}$ | $\mathtt{J}$ | $\mathcal{J}$ | $\mathscr{J}$ | $\mathbb{J}$ |
| 11 | $\mathnormal{K}$ | $\mathrm{K}$ | $\mathbf{K}$ | $\mathsf{K}$ | $\mathit{K}$ | $\mathtt{K}$ | $\mathcal{K}$ | $\mathscr{K}$ | $\mathbb{K}$ |
| 12 | $\mathnormal{L}$ | $\mathrm{L}$ | $\mathbf{L}$ | $\mathsf{L}$ | $\mathit{L}$ | $\mathtt{L}$ | $\mathcal{L}$ | $\mathscr{L}$ | $\mathbb{L}$ |
| 13 | $\mathnormal{M}$ | $\mathrm{M}$ | $\mathbf{M}$ | $\mathsf{M}$ | $\mathit{M}$ | $\mathtt{M}$ | $\mathcal{M}$ | $\mathscr{M}$ | $\mathbb{M}$ |
| 14 | $\mathnormal{N}$ | $\mathrm{N}$ | $\mathbf{N}$ | $\mathsf{N}$ | $\mathit{N}$ | $\mathtt{N}$ | $\mathcal{N}$ | $\mathscr{N}$ | $\mathbb{N}$ |
| 15 | $\mathnormal{O}$ | $\mathrm{O}$ | $\mathbf{O}$ | $\mathsf{O}$ | $\mathit{O}$ | $\mathtt{O}$ | $\mathcal{O}$ | $\mathscr{O}$ | $\mathbb{O}$ |
| 16 | $\mathnormal{P}$ | $\mathrm{P}$ | $\mathbf{P}$ | $\mathsf{P}$ | $\mathit{P}$ | $\mathtt{P}$ | $\mathcal{P}$ | $\mathscr{P}$ | $\mathbb{P}$ |
| 17 | $\mathnormal{Q}$ | $\mathrm{Q}$ | $\mathbf{Q}$ | $\mathsf{Q}$ | $\mathit{Q}$ | $\mathtt{Q}$ | $\mathcal{Q}$ | $\mathscr{Q}$ | $\mathbb{Q}$ |
| 18 | $\mathnormal{R}$ | $\mathrm{R}$ | $\mathbf{R}$ | $\mathsf{R}$ | $\mathit{R}$ | $\mathtt{R}$ | $\mathcal{R}$ | $\mathscr{R}$ | $\mathbb{R}$ |
| 19 | $\mathnormal{S}$ | $\mathrm{S}$ | $\mathbf{S}$ | $\mathsf{S}$ | $\mathit{S}$ | $\mathtt{S}$ | $\mathcal{S}$ | $\mathscr{S}$ | $\mathbb{S}$ |
| 20 | $\mathnormal{T}$ | $\mathrm{T}$ | $\mathbf{T}$ | $\mathsf{T}$ | $\mathit{T}$ | $\mathtt{T}$ | $\mathcal{T}$ | $\mathscr{T}$ | $\mathbb{T}$ |
| 21 | $\mathnormal{U}$ | $\mathrm{U}$ | $\mathbf{U}$ | $\mathsf{U}$ | $\mathit{U}$ | $\mathtt{U}$ | $\mathcal{U}$ | $\mathscr{U}$ | $\mathbb{U}$ |
| 22 | $\mathnormal{V}$ | $\mathrm{V}$ | $\mathbf{V}$ | $\mathsf{V}$ | $\mathit{V}$ | $\mathtt{V}$ | $\mathcal{V}$ | $\mathscr{V}$ | $\mathbb{V}$ |
| 23 | $\mathnormal{W}$ | $\mathrm{W}$ | $\mathbf{W}$ | $\mathsf{W}$ | $\mathit{W}$ | $\mathtt{W}$ | $\mathcal{W}$ | $\mathscr{W}$ | $\mathbb{W}$ |
| 24 | $\mathnormal{X}$ | $\mathrm{X}$ | $\mathbf{X}$ | $\mathsf{X}$ | $\mathit{X}$ | $\mathtt{X}$ | $\mathcal{X}$ | $\mathscr{X}$ | $\mathbb{X}$ |
| 25 | $\mathnormal{Y}$ | $\mathrm{Y}$ | $\mathbf{Y}$ | $\mathsf{Y}$ | $\mathit{Y}$ | $\mathtt{Y}$ | $\mathcal{Y}$ | $\mathscr{Y}$ | $\mathbb{Y}$ |
| 26 | $\mathnormal{Z}$ | $\mathrm{Z}$ | $\mathbf{Z}$ | $\mathsf{Z}$ | $\mathit{Z}$ | $\mathtt{Z}$ | $\mathcal{Z}$ | $\mathscr{Z}$ | $\mathbb{Z}$ |
| ID | 1.mathnormal | 2.mathrm | 3.mathbf | 4.mathsf | 5.mathit | 6.mathtt | 7.mathcal | 8.mathscr | 9.mathbb |
|---|---|---|---|---|---|---|---|---|---|
| 1 | $\mathnormal{a}$ | $\mathrm{a}$ | $\mathbf{a}$ | $\mathsf{a}$ | $\mathit{a}$ | $\mathtt{a}$ | $\mathcal{a}$ | $\mathscr{a}$ | $\mathbb{a}$ |
| 2 | $\mathnormal{b}$ | $\mathrm{b}$ | $\mathbf{b}$ | $\mathsf{b}$ | $\mathit{b}$ | $\mathtt{b}$ | $\mathcal{b}$ | $\mathscr{b}$ | $\mathbb{b}$ |
| 3 | $\mathnormal{c}$ | $\mathrm{c}$ | $\mathbf{c}$ | $\mathsf{c}$ | $\mathit{c}$ | $\mathtt{c}$ | $\mathcal{c}$ | $\mathscr{c}$ | $\mathbb{c}$ |
| 4 | $\mathnormal{d}$ | $\mathrm{d}$ | $\mathbf{d}$ | $\mathsf{d}$ | $\mathit{d}$ | $\mathtt{d}$ | $\mathcal{d}$ | $\mathscr{d}$ | $\mathbb{d}$ |
| 5 | $\mathnormal{e}$ | $\mathrm{e}$ | $\mathbf{e}$ | $\mathsf{e}$ | $\mathit{e}$ | $\mathtt{e}$ | $\mathcal{e}$ | $\mathscr{e}$ | $\mathbb{e}$ |
| 6 | $\mathnormal{f}$ | $\mathrm{f}$ | $\mathbf{f}$ | $\mathsf{f}$ | $\mathit{f}$ | $\mathtt{f}$ | $\mathcal{f}$ | $\mathscr{f}$ | $\mathbb{f}$ |
| 7 | $\mathnormal{g}$ | $\mathrm{g}$ | $\mathbf{g}$ | $\mathsf{g}$ | $\mathit{g}$ | $\mathtt{g}$ | $\mathcal{g}$ | $\mathscr{g}$ | $\mathbb{g}$ |
| 8 | $\mathnormal{h}$ | $\mathrm{h}$ | $\mathbf{h}$ | $\mathsf{h}$ | $\mathit{h}$ | $\mathtt{h}$ | $\mathcal{h}$ | $\mathscr{h}$ | $\mathbb{h}$ |
| 9 | $\mathnormal{i}$ | $\mathrm{i}$ | $\mathbf{i}$ | $\mathsf{i}$ | $\mathit{i}$ | $\mathtt{i}$ | $\mathcal{i}$ | $\mathscr{i}$ | $\mathbb{i}$ |
| 10 | $\mathnormal{j}$ | $\mathrm{j}$ | $\mathbf{j}$ | $\mathsf{j}$ | $\mathit{j}$ | $\mathtt{j}$ | $\mathcal{j}$ | $\mathscr{j}$ | $\mathbb{j}$ |
| 11 | $\mathnormal{k}$ | $\mathrm{k}$ | $\mathbf{k}$ | $\mathsf{k}$ | $\mathit{k}$ | $\mathtt{k}$ | $\mathcal{k}$ | $\mathscr{k}$ | $\mathbb{k}$ |
| 12 | $\mathnormal{l}$ | $\mathrm{l}$ | $\mathbf{l}$ | $\mathsf{l}$ | $\mathit{l}$ | $\mathtt{l}$ | $\mathcal{l}$ | $\mathscr{l}$ | $\mathbb{l}$ |
| 13 | $\mathnormal{m}$ | $\mathrm{m}$ | $\mathbf{m}$ | $\mathsf{m}$ | $\mathit{m}$ | $\mathtt{m}$ | $\mathcal{m}$ | $\mathscr{m}$ | $\mathbb{m}$ |
| 14 | $\mathnormal{n}$ | $\mathrm{n}$ | $\mathbf{n}$ | $\mathsf{n}$ | $\mathit{n}$ | $\mathtt{n}$ | $\mathcal{n}$ | $\mathscr{n}$ | $\mathbb{n}$ |
| 15 | $\mathnormal{o}$ | $\mathrm{o}$ | $\mathbf{o}$ | $\mathsf{o}$ | $\mathit{o}$ | $\mathtt{o}$ | $\mathcal{o}$ | $\mathscr{o}$ | $\mathbb{o}$ |
| 16 | $\mathnormal{p}$ | $\mathrm{p}$ | $\mathbf{p}$ | $\mathsf{p}$ | $\mathit{p}$ | $\mathtt{p}$ | $\mathcal{p}$ | $\mathscr{p}$ | $\mathbb{p}$ |
| 17 | $\mathnormal{q}$ | $\mathrm{q}$ | $\mathbf{q}$ | $\mathsf{q}$ | $\mathit{q}$ | $\mathtt{q}$ | $\mathcal{q}$ | $\mathscr{q}$ | $\mathbb{q}$ |
| 18 | $\mathnormal{r}$ | $\mathrm{r}$ | $\mathbf{r}$ | $\mathsf{r}$ | $\mathit{r}$ | $\mathtt{r}$ | $\mathcal{r}$ | $\mathscr{r}$ | $\mathbb{r}$ |
| 19 | $\mathnormal{s}$ | $\mathrm{s}$ | $\mathbf{s}$ | $\mathsf{s}$ | $\mathit{s}$ | $\mathtt{s}$ | $\mathcal{s}$ | $\mathscr{s}$ | $\mathbb{s}$ |
| 20 | $\mathnormal{t}$ | $\mathrm{t}$ | $\mathbf{t}$ | $\mathsf{t}$ | $\mathit{t}$ | $\mathtt{t}$ | $\mathcal{t}$ | $\mathscr{t}$ | $\mathbb{t}$ |
| 21 | $\mathnormal{u}$ | $\mathrm{u}$ | $\mathbf{u}$ | $\mathsf{u}$ | $\mathit{u}$ | $\mathtt{u}$ | $\mathcal{u}$ | $\mathscr{u}$ | $\mathbb{u}$ |
| 22 | $\mathnormal{v}$ | $\mathrm{v}$ | $\mathbf{v}$ | $\mathsf{v}$ | $\mathit{v}$ | $\mathtt{v}$ | $\mathcal{v}$ | $\mathscr{v}$ | $\mathbb{v}$ |
| 23 | $\mathnormal{w}$ | $\mathrm{w}$ | $\mathbf{w}$ | $\mathsf{w}$ | $\mathit{w}$ | $\mathtt{w}$ | $\mathcal{w}$ | $\mathscr{w}$ | $\mathbb{w}$ |
| 24 | $\mathnormal{x}$ | $\mathrm{x}$ | $\mathbf{x}$ | $\mathsf{x}$ | $\mathit{x}$ | $\mathtt{x}$ | $\mathcal{x}$ | $\mathscr{x}$ | $\mathbb{x}$ |
| 25 | $\mathnormal{y}$ | $\mathrm{y}$ | $\mathbf{y}$ | $\mathsf{y}$ | $\mathit{y}$ | $\mathtt{y}$ | $\mathcal{y}$ | $\mathscr{y}$ | $\mathbb{y}$ |
| 26 | $\mathnormal{z}$ | $\mathrm{z}$ | $\mathbf{z}$ | $\mathsf{z}$ | $\mathit{z}$ | $\mathtt{z}$ | $\mathcal{z}$ | $\mathscr{z}$ | $\mathbb{z}$ |
3.3. a的四种写法
# four ways to set the letter a in a bold sans-serif font:
% Text Math:
\textbf{\textsf{a}} $\bm{\mathsf{a}}$
\bfseries \textsf{a} \mathversion{bold} $\mathsf{a}$
4. 9 Matrix
\begin{bmatrix}
a&b\\
c&d
\end{bmatrix}
5. 10 Table
\begin{array}{c|c}
\text{Year} & \text{Sand Area}(\text{km}^2) \\
\hline
2000 & 90.0\\
2010 & 100.0\\
\end{array}\\
6. 示例
6.1. Ex.1
Let $\mathcal{T}$ be a topological space, a basis is defined as