KaTeX 数学符号列表[通俗易懂]

B Beta B Beta

β beta β beta

Υ Upsilon Υ Upsilon

υ upsilon υ upsilon

Γ Gamma Γ Gamma

γ gamma γ gamma

Φ Phi Φ Phi

ϕ phi ϕ phi

Δ Delta Δ Delta

δ delta δ delta

X Chi X Chi

χ chi χ chi

E Epsilon E Epsilon

ϵ epsilon ϵ epsilon

Ψ Psi Ψ Psi

ψ psi ψ psi

Z Zeta Z Zeta

ζ zeta ζ zeta

Ω Omega Ω Omega

ω omega ω omega

H Eta H Eta

η eta η eta

Π varPi Π varPi

ϖ varpi ϖ varpi

Θ Theta Θ Theta

θ theta θ theta

Σ varSigma Σ varSigma

ς varsigma ς varsigma

I Iota I Iota

ι iota ι iota

Θ varTheta Θ varTheta

ϑ vartheta ϑ vartheta

K Kappa K Kappa

κ kappa κ kappa

Φ varPhi Φ varPhi

φ varphi φ varphi

Λ Lambda Λ Lambda

λ lambda λ lambda

Γ varGamma Γ varGamma

ε varepsilon ε varepsilon

M Mu M Mu

μ mu μ mu

Δ varDelta Δ varDelta

ϰ varkappa ϰ varkappa

N Nu N Nu

ν nu ν nu

Λ varLambda Λ varLambda

ϑ thetasym ϑ thetasym

Ξ Xi Ξ Xi

ξ xi ξ xi

Ξ varXi Ξ varXi

ϱ varrho ϱ varrho

O Omicron O Omicron

ο omicron ο omicron

Υ varUpsilon Υ varUpsilon

ϝ digamma ϝ digamma

Π Pi Π Pi

π pi π pi

Ψ varPsi Ψ varPsi

P Rho P Rho

ρ rho ρ rho

Ω varOmega Ω varOmega

Σ Sigma Σ Sigma

σ sigma σ sigma

℧ mho ℧ mho

ı imath ı imath

∇ nabla ∇ nabla

ℑ Im ℑ Im

R Reals R Reals

ȷ jmath ȷ jmath

∂ partial ∂ partial

ℑ image ℑ image

℘ wp ℘ wp

ℵ aleph ℵ aleph

⅁ Game ⅁ Game

k Bbbk k Bbbk

℘ weierp ℘ weierp

ℵ alef ℵ alef

Ⅎ Finv Ⅎ Finv

N N N N

Z Z Z Z

ℵ alefsym ℵ alefsym

C cnums C cnums

N natnums N natnums

a ˚ text{aa} a˚ text{aa}

ℶ beth ℶ beth

C Complex C Complex

R R R R

A ˚ text{AA} A˚ text{AA}

ℷ gimel ℷ gimel

ℓ ell ℓ ell

ℜ Re ℜ Re

æ text{ae} æ text{ae}

ℸ daleth ℸ daleth

ℏ hbar ℏ hbar

ℜ real ℜ real

Æ text{AE} Æ text{AE}

ð eth ð eth

ℏ hslash ℏ hslash

R reals R reals

œ text{oe} œ text{oe}

a ˉ ; a b i ‾ bar{a};overline{a bi} aˉ;a bi​

共轭

bar{a}; overline{a bi}

A B ‾ underline{AB} AB​

underline{AB}

a ⃗ , A B → ; a c ⇀ vec{a},overrightarrow{AB};overrightharpoon{ac} a ,AB ;ac

向量

vec{a},overrightarrow{AB};overrightharpoon{ac}

A B → underrightarrow{AB} AB​

underrightarrow{AB}

A B ← ; a c ↼ ; A B ← overleftarrow{AB};overleftharpoon{ac};underleftarrow{AB} AB ;ac ; AB​

overleftarrow{AB};;overleftharpoon{ac};underleftarrow{AB}

T ↔ overleftrightarrow{T} T

张量

overleftrightarrow{T}

T ⇉ overset{rightrightarrows}{T} T⇉

张量并矢

overset{rightrightarrows}{T}

A B ↔ underleftrightarrow{AB} AB​

underleftrightarrow{AB}

A B ⇒ Overrightarrow{AB} AB

Overrightarrow{AB}

b a dfrac{b}{a} ab​

分数

frac{b}{a}; dfrac{b}{a}

a 1 1 b cfrac{a}{1 cfrac{1}{b}} 1 b1​a​

复合分式

cfrac{a}{1 cfrac{1}{b}}

x ; x n sqrt{x}; sqrt[n]{x} x ​;nx ​

开方

sqrt{x}; sqrt[n]{x}

a n a^n an

指数

a^n

a n a_n an​

下标

a_n

= ! stackrel{!}{=} =!

堆叠

stackrel{!}{=}

= ! overset{!}{=} =!

上方

overset{!}{=}

= ! underset{!}{=} !=​

下方

underset{!}{=}

a b a atop b ba​

a atop b

a b c araisebox{0.25em}{b}c abc

araisebox{0.25em}{b}c

f ∘ g f circ g f∘g

复合函数

f circ g

θ ^ hat{theta} θ^

坐标基

hat{theta};^{theta}

a c ^ widehat{ac} ac

夹角

widehat{ac}

a ˘ breve{a} a˘

breve{a}

a ˇ ; a c ˇ check{a};widecheck{ac} aˇ;ac

check{a};widecheck{ac}

a ~ ; a c ~ ; A B ~ tilde{a};widetilde{ac};utilde{AB} a~;ac ; AB​

波浪

tilde{a};widetilde{ac};utilde{AB}

a ˊ acute{a} aˊ

acute{a}

a ˋ grave{a} aˋ

grave{a}

A B ⏠ ; A B ⏡ overgroup{AB};undergroup{AB} AB ; AB​

overgroup{AB};undergroup{AB}

= = =

is equal to

=

≈ approx ≈

is approximately equal to

approx

plus

− – −

minus

–

± ; ∓ pm; mp ±;∓

plus-minus; minus-plus

pm; mp

× times ×

multiplied by;cross product

times

⋅ cdot ⋅

dot product

cdot; centerdot

∗ * ∗

*;ast

÷ ; / div; / ÷;/

divided by

div; /

< < <

is less than

<;lt

> > >

is greater than

>;gt

≪ ; ⋘ ll;lll ≪;⋘

远小于

lllll

≫ ; ⋙ gg;ggg ≫;⋙

远大于

gg;ggg

⩾ ; ≥ geqslant;ge ⩾;≥

大于等于

geqslantge

⩽ ; ≤ leqslant;le ⩽;≤

小于等于

leqslant;le

∝ propto ∝

正比于

propto

≜ triangleq ≜

定义

triangleq

≠ ; ∉ not=;notin ​=;​∈

前方加not否定

not=;notin

∑ k = 0 n ∁ n k displaystylesum_{k=0}^n complement^k_n k=0∑n​∁nk​

求和

displaystylesum_{k=0}^n complement^k_n

∏ prod ∏

求积

prod

⨿ amalg ⨿

合并

amalg

∣ a ∣ mid a mid ∣a∣

绝对值

vert; mid; |;vert; rvert

∥ a ∥ |a| ∥a∥

范数，模

Vert; |; lVert ;rVert

⌈ a ⌉ lceil arceil ⌈a⌉

ceiling

lceil arceil

⌊ a ⌋ lfloor arfloor ⌊a⌋

floor

lfloor arfloor

⌊2.1⌋ = 2

⌊ a ⌉ lfloor arceil ⌊a⌉

最接近的整数

lfloor arceil

⌊2.6⌉ = 3

⎰ ⎱ lmoustachermoustache ⎰⎱

胡须

lmoustachermoustache

┌ ┐ ulcornerurcorner ┌┐

ulcornerurcorner

└ ┘ llcornerlrcorner └┘

llcornerlrcorner

↑ ; ↓ ; ↕ uparrow;downarrow;updownarrow ↑;↓;↕

uparrow;downarrow;updownarrow

⇑ ; ⇓ ; ⇕ Uparrow;Downarrow;Updownarrow ⇑;⇓;⇕

uparrow;downarrow;updownarrow

§ text{sect} §

分节

text{sect}

⋆ star ⋆

星号

star

5 cancel{5} 5 ​

划线

cancel{5}

5 bcancel{5} 5 ​

划线

bcancel{5}

a b c xcancel{abc} abc

划线

xcancel{5}

5 sout{5} 5

划线

sout{5}

π = c d boxed{pi=frac c d} π=dc​​

方框

boxed{pi=frac c d}

a b c ⏞ note overbrace{a b c}^{text{note}} a b c ​note​

上备注

overbrace{a b c}^{text{note}}

a b c ⏟ note underbrace{a b c}_{text{note}} note a b c​​

下备注

underbrace{a b c}_{text{note}}

arccos ⁡ arccos arccos arccos

coth ⁡ coth coth coth

log ⁡ log log log

gcd ⁡ gcd gcd gcd

arctan ⁡ arctan arctan arctan

csc ⁡ csc csc csc

sec ⁡ sec sec sec

inf ⁡ inf inf inf

arctg ⁡ arctg arctg arctg

ctg ⁡ ctg ctg ctg

sin ⁡ sin sin sin

lim ⁡ lim lim lim

arcctg ⁡ arcctg arcctg arcctg

cth ⁡ cth cth cth

sinh ⁡ sinh sinh sinh

lim inf ⁡ liminf liminf liminf

arg ⁡ arg arg arg

deg ⁡ deg deg deg

sh ⁡ sh sh sh

lim sup ⁡ limsup limsup limsup

ch ⁡ ch ch ch

dim ⁡ dim dim dim

tan ⁡ tan tan tan

max ⁡ max max max

cos ⁡ cos cos cos

exp ⁡ exp exp exp

tanh ⁡ tanh tanh tanh

min ⁡ min min min

cosec ⁡ cosec cosec cosec

hom ⁡ hom hom hom

tg ⁡ tg tg tg

Pr ⁡ Pr Pr Pr

cosh ⁡ cosh cosh cosh

ker ⁡ ker ker ker

th ⁡ th th th

sup ⁡ sup sup sup

cot ⁡ cot cot cot

lg ⁡ lg lg lg

f ⁡ operatorname{f} f operatorname{f}

arg ⁡ max ⁡ argmax argmax argmax

arg ⁡ min ⁡ argmin argmin argmin

∵ because ∵

因为

because

∴ therefore ∴

所以

therefore

¬ ; ∼ lnot; sim ¬;∼

逻辑非(negation)

neg; lnot; sim

¬ ( ¬ A )    ⟺    A lnot(lnot A)iff A ¬(¬A)⟺A

∧ land ∧

逻辑与

land

n < 4 ∧ n > 2 ⇔ n = 3 when n is a natural number.

∨ lor ∨

逻辑或

lor

n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number.

⊕ ; ⊻ oplus; veebar ⊕;⊻

异或

oplus; veebar

a ⊕ b = ( ¬ a ∧ b ) ∨ ( a ∧ ¬ b ) aoplus b=(lnot aland b)lor(aland lnot b) a⊕b=(¬a∧b)∨(a∧¬b)

⟺    ; ↔ iff; leftrightarrow ⟺;↔

双条件，等价关系，当且仅当(if and only if)

iff; leftrightarrow

⇒ ; → Rarr; rarr ⇒;→

条件运算,if … then

Rarr; rarr ;to

x = 6 ⇒ x 2 = 36 x=6Rightarrow x^2=36 x=6⇒x2=36

⇐ ; ← Larr; larr ⇐;←

左箭头

Larr; larr; gets

: = ; : ⇔ :=; :Leftrightarrow :=;:⇔

定义

:=

⟹    ;    ⟸    implies; impliedby ⟹;⟸

implies; impliedby

∀ forall ∀

任意

forall

∀ n ∈ ℕ, n2 ≥ n

∃ exists ∃

存在

exists

∃ n ∈ ℕ: n is even

∃ ! exists! ∃!

唯一存在

exists!

∃! n ∈ ℕ: n 5 = 2n.

⊨ vDash ⊨

满足符

vDash

A ⊨ B AvDash B A⊨B

⊢ vdash ⊢

推断出

vdash

A → B ⊢ ¬B → ¬A

□ square □

拟态词必然

square

◊ Diamond ◊

拟态词可能

Diamond

R ∘ S R circ S R∘S

复合关系

R circ S

{ x ∣ P ( x ) } {xvert P(x)} { x∣P(x)}

集合

{xmid P(x)}

U ˚ mathring{U} U˚

邻域

mathring{U}

⊎ uplus ⊎

多重集

uplus

⊂ subset ⊂

真子集

subset

⊆ subseteq ⊆

子集

subseteq

⊃ supset ⊃

真父集

supset

⊇ supseteq ⊇

父集

supseteq

∈ in ∈

in

∋ ni ∋

ni

∩ cap ∩

交集

cap

∪ cup ∪

并集

cup

∖ setminus ∖

差集

setminus

c a r d ( A ) mathrm{card}(A) card(A)

元素个数

mathrm{card}(A)

∅ ; ∅ emptyset; varnothing ∅;∅

空集

emptyset; varnothing

N N N

自然数

N

Z Z Z

整数

Z

R R R

实数

R;Reals

ℑ Im ℑ

虚数

Im; Image

C Complex C

复数

Complex

n ! n! n!

阶乘

n!

( n k ) binom{n}{k} (kn​), [ n k ] {nbrack k} [kn​]

二项式系数

binom{n}{k}; dbinom{n}{k}; {n choose k}; nbrack k

A m n A^n_m Amn​

排列(Arrangement)

A^n_m

∁ m n complement^n_m ∁mn​

组合

complement^n_m

X ∼ N ( μ , σ 2 ) Xsim N(mu,sigma^2) X∼N(μ,σ2)

服从分布

sim

⟨φ|ψ⟩

左矢量,右矢量

langlerangle

{ n k } {nbrace k} { kn​}

{nbrace k}

[ n k ] {nbrack k} [kn​]

{nbrack k}

∽ backsim ∽

相似三角形

backsim

⋍ backsimeq ⋍

backsimeq

= ∽ overset{backsim}{=} =∽

全等三角形

overset{backsim}{=}

∥ parallel ∥

平行

parallel

∦ nparallel ∦

不平行

nparallel

⊥ bot ⊥

垂直

bot

A B ‾ overline{AB} AB

直线

overline{AB}

A B undefined overlinesegment{AB} AB

线段

overlinesegment{AB}

A B undefined underlinesegment{AB} AB​

underlinesegment{AB}

A B ⌢ overset{frown}{AB} AB⌢

弧

overset{frown}{AB}

⊙ odot ⊙

圆

odot

◯ bigcirc ◯

bigcirc

⊡ boxdot ⊡

boxdot

□ square □

矩形

square

R t △ mathrm{Rt}triangle Rt△

直角三角形

mathrm{Rt}triangle

◊ Diamond ◊

菱形

Diamond

∠ angle ∠

角

angle

∡ measuredangle ∡

measuredangle

90 ° 90degree 90°

角度

90degree

← gets ←

gets

→ to →

趋向于

to

f : X → Y f:Xto Y f:X→Y

∞ infty ∞

无穷大

infty

lim ⁡ lim lim

极限

limlimits_{xto infty} f(x)=1

lim ⁡ x → ∞ f ( x ) = 1 limlimits_{xto infty} f(x)=1 x→∞lim​f(x)=1

x ˙ dot{x} x˙

导数

dot{x}

x ¨ ddot{x} x¨

二阶导

ddot{x}

x ′ x’ x′

导数

x’; x^prime

x ′ ′ x” x′′

二阶导

x’’

x ( n ) x^{(n)} x(n)

n阶导

x^{(n)}

∂ partial ∂

偏导数

partial

d x mathrm{d}x dx

微分

mathrm{d}x

∫ int ∫

积分

int

∫ x 2 d x = x 3 3 C ∫ a b x 2 d x = b 3 − a 3 3 int x^2mathrm{d}x =dfrac{x^3}{3} C \ int_a^b x^2mathrm{d}x =dfrac{b^3-a^3}{3} ∫x2dx=3x3​ C∫ab​x2dx=3b3−a3​

∬ iint ∬

积分

iint

∭ iiint ∭

积分

iiint

∮ oint ∮

曲线积分

oint

∮ C 1 z d z = 2 π i oint_C frac{1}{z}mathrm{d}z=2pi i ∮C​z1​dz=2πi

∯ oiint ∬ ​

积分

oiint

∰ oiiint ∭ ​

积分

oiiint

∇ nabla ∇

微分算子

nabla

∇ ⋅ v ⃗ = ∂ v ∂ x ∂ v ∂ y ∂ v ∂ z nablacdotvec{v}=dfrac{partial v}{partial x} dfrac{partial v}{partial y} dfrac{partial v}{partial z} ∇⋅v =∂x∂v​ ∂y∂v​ ∂z∂v​

Δ Delta Δ

拉普拉斯算子

Delta

Δ f = ∇ 2 f = ∇ ⋅ ∇ f Delta f=nabla ^{2}f=nabla cdot nabla f Δf=∇2f=∇⋅∇f

□ Box □

非欧几里得拉普拉斯算子

Box

□ = 1 c 2 ∂ 2 ∂ t 2 − ∂ 2 ∂ x 2 − ∂ 2 ∂ y 2 − ∂ 2 ∂ z 2 Box=dfrac{1}{c^2}dfrac{partial^2}{partial t^2}-dfrac{partial^2}{partial x^2}-dfrac{partial^2}{partial y^2}-dfrac{partial^2}{partial z^2} □=c21​∂t2∂2​−∂x2∂2​−∂y2∂2​−∂z2∂2​

f ( x ) = { a if b c if d f(x)=begin{cases} a &text{if } b \ c &text{if } d end{cases} f(x)={ ac​if bif d​

定义方程

f(x)=begin{cases} a &text{if } b \ c &text{if } d end{cases}

10 x 3 y = 2 3 x 13 y = 4 begin{alignedat}{2} 10&x &3&y = 2 \ 3&x &13&y = 4 end{alignedat} 103​x x ​313​y=2y=4​

方程组

begin{alignedat}{2} 10&x &3&y = 2 \ 3&x &13&y = 4 end{alignedat}

f ( x ) = ( m n ) 2 = m 2 2 m n 2 begin{aligned} f(x) &=(m n)^2 \ & =m^2 2m n^2 end{aligned} f(x)​=(m n)2=m2 2m n2​

多行等式

begin{aligned} f(x) &=(m n)^2 \ & =m^2 2m n^2 end{aligned}

a b c d begin{matrix} a & b \ c & dend{matrix} ac​bd​

数组

begin{matrix} a & b \ c & dend{matrix}

a b c d begin{array}{cc} a & b \ c & dend{array} ac​bd​

数组

begin{array}{cc} a & b \ c & dend{array}

( a b c d ) begin{pmatrix} a & b \ c & dend{pmatrix} (ac​bd​)

矩阵

begin{pmatrix} a & b \ c & d end{pmatrix}

[ a b c d ] begin{bmatrix} a & b \ c & dend{bmatrix} [ac​bd​]

矩阵

begin{bmatrix} a & b \ c & d end{bmatrix}

∣ a b c d ∣ begin{vmatrix} a & b \ c & dend{vmatrix} ∣∣∣∣​ac​bd​∣∣∣∣​

行列式

begin{vmatrix} a & b \ c & d end{vmatrix}

∥ a b c d ∥ begin{Vmatrix} a & b \ c & dend{Vmatrix} ∥∥∥∥​ac​bd​∥∥∥∥​

范式，模

begin{Vmatrix} a & b \ c & d end{Vmatrix}

{ a b c d } begin{Bmatrix}a & b \ c & dend{Bmatrix} { ac​bd​}

begin{Bmatrix}a & b \ c & dend{Bmatrix}

a b c d e f g h i defarraystretch{1.5} begin{array}{c:c:c} a & b & c \ hline d & e & f \ hdashline g & h & iend{array} adg​beh​cfi​​

defarraystretch{1.5} begin{array}{c:c:c} a & b & c \ hline d & e & f \ hdashline g & h & iend{array}

→ u n d e r o v e r xrightarrow[under]{over} over under​

初等变换

xrightarrow[under]{over}

A ≅ B Acong B A≅B

矩阵等价

Acong B

A ∼ B Asim B A∼B

矩阵相似

Asim B

A ≃ B Asimeq B A≃B

矩阵合同

Asimeq B

A ˉ bar{A} Aˉ

bar{A}

A ∗ A^* A∗

伴随矩阵

A^*

det ⁡ A ; ∣ A ∣ det A;vert A vert detA;∣A∣

矩阵的行列式

det A

d i a g ( a 1 , a 2 , a 3 ) mathrm{diag}(a_1,a_2,a_3) diag(a1​,a2​,a3​)

对角阵

mathrm{diag}(a_1,a_2,a_3)

A ⊗ B Aotimes B A⊗B

克罗内克积

otimes

⋯ cdots ⋯

横点

cdots

⋮ vdots ⋮

竖点

vdots

⋱ ddots ⋱

对角点

ddots

b ( m o d m ) bpmod m b(modm)

bpmod m

x ( a ) x pod a x(a)

x pod a

a   m o d   b a bmod b amodb

a bmod b

≡ equiv ≡

同余关系

equiv

a ≡ b ( m o d m ) aequiv bpmod m a≡b(modm)

⋗ gtrdot ⋗

gtrdot

⋖ lessdot ⋖

lessdot

⊺ intercal ⊺

区间

intercal

⊳ rhd ⊳

双方关系对立

rhd

R ⊳ S = R − R ⋉ S Rrhd S=R-Rltimes S R⊳S=R−R⋉S

⊲ lhd ⊲

正规子群

lhd

Z ( G ) ⊲ G Z(G) lhd G Z(G)⊲G

⊵ unrhd ⊵

unrhd

⊴ unlhd ⊴

unlhd

⋋ leftthreetimes ⋋

leftthreetimes

⋌ rightthreetimes ⋌

rightthreetimes

⋊ rtimes ⋊

rtimes

⋉ ltimes ⋉

ltimes

≺ prec ≺

卡普可约

prec

If L1 ≺ L2 and L2 ∈ P, then L1 ∈ P

≻ succ ≻

succ

∣ mid ∣

分解

mid

Since 15 = 3 × 5, it is true that 3 | 15 and 5 | 15

∤ nmid ∤

nmid