MindMap Gallery LaTeX
This is a mind map about LaTeX, mainly including functional characters, special symbols, combinators, Mathematical formulas, functions, brackets, matrices, equations, etc.
Edited at 2023-12-19 21:53:11Discover how Aeon can navigate the competitive online landscape with a strategic SWOT analysis. This comprehensive overview highlights Aeon’s strengths, such as its strong brand recognition, omnichannel capabilities, and customer loyalty programs, alongside its weaknesses, including digital maturity gaps and cost structure challenges. Opportunities for growth include enhancing e-commerce competitiveness and leveraging data-driven strategies, while threats from online-first players and market dynamics require attention. Explore how Aeon can strengthen its market position through innovation and customer-centric approaches in the ever-evolving retail environment.
Discover how Aeon effectively tailors its offerings to meet the diverse needs of family-oriented consumers through a comprehensive Segmentation, Targeting, and Positioning (STP) analysis. Our approach begins with demographic segmentation, examining family life stages, household sizes, income levels, and parent age bands to identify distinct consumer groups. Geographic segmentation highlights store catchment types and community characteristics, while psychographic segmentation delves into family values and lifestyle orientations. Behavioral segmentation focuses on shopping missions, price sensitivity, and channel preferences. Finally, needs-based segmentation reveals core family needs related to value and budget considerations. Join us as we explore these insights to enhance family shopping experiences at Aeon.
Discover the dynamics of sneaker transactions with our Kream Sneaker Consumption Scene Analysis Template. This comprehensive framework aims to visualize the purchasing and consumption journeys of sneakers, identifying key demand drivers and obstacles. It covers user behavior within Kream and external influences, targeting various sneaker categories over specific timeframes and regions. The analysis defines user segments, including collectors, resellers, sneakerheads, casual trend followers, and gift purchasers, each with unique values and KPIs. It outlines the consumption journey from awareness to resale, highlighting critical touchpoints such as search, purchase, inspection, and sharing experiences. Key performance indicators are established to measure engagement and satisfaction throughout the process. Join us in exploring the intricate world of sneaker trading!
Discover how Aeon can navigate the competitive online landscape with a strategic SWOT analysis. This comprehensive overview highlights Aeon’s strengths, such as its strong brand recognition, omnichannel capabilities, and customer loyalty programs, alongside its weaknesses, including digital maturity gaps and cost structure challenges. Opportunities for growth include enhancing e-commerce competitiveness and leveraging data-driven strategies, while threats from online-first players and market dynamics require attention. Explore how Aeon can strengthen its market position through innovation and customer-centric approaches in the ever-evolving retail environment.
Discover how Aeon effectively tailors its offerings to meet the diverse needs of family-oriented consumers through a comprehensive Segmentation, Targeting, and Positioning (STP) analysis. Our approach begins with demographic segmentation, examining family life stages, household sizes, income levels, and parent age bands to identify distinct consumer groups. Geographic segmentation highlights store catchment types and community characteristics, while psychographic segmentation delves into family values and lifestyle orientations. Behavioral segmentation focuses on shopping missions, price sensitivity, and channel preferences. Finally, needs-based segmentation reveals core family needs related to value and budget considerations. Join us as we explore these insights to enhance family shopping experiences at Aeon.
Discover the dynamics of sneaker transactions with our Kream Sneaker Consumption Scene Analysis Template. This comprehensive framework aims to visualize the purchasing and consumption journeys of sneakers, identifying key demand drivers and obstacles. It covers user behavior within Kream and external influences, targeting various sneaker categories over specific timeframes and regions. The analysis defines user segments, including collectors, resellers, sneakerheads, casual trend followers, and gift purchasers, each with unique values and KPIs. It outlines the consumption journey from awareness to resale, highlighting critical touchpoints such as search, purchase, inspection, and sharing experiences. Key performance indicators are established to measure engagement and satisfaction throughout the process. Join us in exploring the intricate world of sneaker trading!
LaTeX
function characters
1. $: Indicates the start and end of math mode.
\$
2. %: Represents the comment symbol, used to add comments in the code.
\%
3. &: represents the column separator in the table.
\&
4. #: Represents the parameter identifier in the macro definition.
\#
5. _: represents the subscript symbol, used to represent subscripts in mathematical formulas.
\_
a_2
a_{i,j}
\tilde{A}_2
6. ^: represents the superscript symbol, used to represent superscript in mathematical formulas.
\texttt{^}
a^2
a^{2 2}
x'
x^\prime
x\prime
x_2^3
{}_1^2\!X_3^4
7. { }: represents a grouping symbol, used to combine a group of commands or symbols together.
\{
\}
\lbrace
\rbrace
8. \: represents the escape symbol, used to enter some special characters
\texttt{\\}
\text{\\}
\backslash
9. ~: Indicates non-line-breaking spaces.
\sim
spacing
horizontal spacing
One meter wide:\quad
Two meters wide: \qquad
1/3m wide:\
2/7m wide:\;
1/6m wide: \,
Clinging:\!
Custom:\hspace{6cm}
Blocking distance is ignored: \hspace*{}
vertical spacing
\vspace{-1em}
\vspace{1em}
Rubber length
\fill
\hfill
\hspace{\fill}
special symbols
Greek alphabet
A\alpha
Αα
/'ælfə/
alpha
alpha
B\beta
Bβ
/'bi:tə/ or /'beɪtə/
beta
Beta
\Gamma\gamma
Γγ
/'gæmə/
gamma
gamma[3]/gamma
\Delta\delta
Δδ
/'deltə/
delta
delta
\Epsilon\epsilon\varepsilon
Εε,ϵ
/'epsɪlɒn/
epsilon
Epsilon
Z\zeta
Ζζ
/'zi:tə/
zeta
Zeta
E\eta
H
/'i:tə/
eta
ita
\Theta\theta\vartheta
Θθ
/'θi:tə/
theta
west tower
I\iota
Ιι
/aɪ'əʊtə/
iota
about (yāo) tower
\Kappa\kappa\varkappa
Kκ
/'kæpə/
kappa
Kappa
\Lambda\lambda
∧λ
/'læmdə/
lambda
lambda
M\mu
Μμ
/mju:/
mu
absurd
N u
Νν
/nju:/
nu
New
\Xi\xi
Ξξ
Greece /ksi/ British and American /ˈzaɪ/ or /ˈsaɪ/
xi
Kersey
O\omicron
Οο
/əuˈmaikrən/or /ˈɑmɪˌkrɑn/
omicron
Omicron [3]/Omicron
\Pi\pi\varpi
∏π
/paɪ/
pi
group
P\rho\varrho
Ρρ
/rəʊ/
rho
soft
\Sigma\sigma\varsigma
∑σ
/'sɪɡmə/
sigma
sigma
T\tau
Ττ
/tɔ:/ or /taʊ/
Tau
pottery
\Upsilon\upsilon
Υυ
/ˈipsɪlon/ or /ˈʌpsɪlɒn/
upsilon
Upsilon
\Phi\phi\varphi
Φφ
/faɪ/
phi
Fiji
X\chi
Χχ
/kaɪ/
chi
Hope [3]/kai
\Psi\psi
Ψψ
/psaɪ/
psi
Pusey
\Omega\omega
Ωω
/'əʊmɪɡə/ or /oʊ'meɡə/
omega
Omega/Omega
\eth
\S
\dagger
\ddagger
\star
\circ
\bigodot
\bullet
\cdot
\ldots
\smile
\frown
\wr
\oplus
\bigoplus
\boxplus
\times
\otimes
\bigotimes
\boxtimes
\div
\triangleleft
\triangleright
\triangle
\Delta
abla
\angle
\diamondsuit
\Diamond
\Box
\bot
\top
\vdash
\vDash
\Vdash
\models
\vert
\|
\lVert
\rVert
\infty
\imath
\hbar
\ell
\mho
\Finv
\Re
\Im
\wp
\complement
\digamma
\partial x
\heartsuit
\clubsuit
\spadesuit
1. \flat
atural
\sharp
\Game
gather
\forall
\exists
\empty
\emptyset
\varnothing
\in
i
ot\in
otin
\subset
\subseteq
\supset
\supsteq
\cap
\bigcap
\cup
\bigcup
\biguplus
\sqsubset
\sqsubseteq
\sqsupset
\sqsupsteq
\sqcap
\sqcup
\bigsqcup
intersection
\bigcap_1^{n} p
union
\bigcup_1^{k} p
relation symbol
\simeq
\cong
>
\ge
\geqq
\gg
\ggg
<
\leq
\leqq
\ll
\lll
=
\equiv
\lessgtr
\gtrless
\perp
\pm
\mp
x ot\equiv N
x e A
x eq C
t\propto v
\Delta ABC\sim\Delta XYZ
\therefore
\because
logic
\land
\wedge
\bigwedge
\lor
\vee
\bigvee
\lnot
eg
\setminus
\smallsetminus
arrow symbol
\leftarrow
\gets
\rightarrow
\to
\mapsto
\longmapsto
\longleftarrow
\longrightarrow
\leftrightarrow
\hookrightarrow
\hookleftarrow
earrow
\searrow
\swarrow
warrow
\uparrow
\downarrow
\updownarrow
\rightharpoonup
\rightharpoondown
\leftharpoonup
\leftharpoondown
\upharpoonleft
\upharpoonright
\downharpoonleft
\downharpoonright
\Leftarrow
\Rightarrow
\Leftrightarrow
\Longleftarrow
\Longrightarrow
\Longleftrightarrow (or \iff)
\Uparrow
\Downarrow
\Updownarrow
Combinator
phonetic notation
\bar{x}
\acute{\eta}
\check{\alpha}
\grave{\eta}
\breve{a}
\hat{\alpha}
\tilde{\iota}
\dot{a}
\ddot{y}
vector
\vec{c}
\overleftarrow{a b}
\overrightarrow{c d}
\widehat{e f g}
upper arc
\overset{\frown} {AB}
Overline
\overline{h i j}
Underline
\underline{k l m}
upper bracket
\overbrace{1 2 \cdots 100}
\begin{matrix} 5050 \\ \overbrace{ 1 2 \cdots 100 }\end{matrix}
lower bracket
\underbrace{a b \cdots z}
\begin{matrix} \underbrace{ a b \cdots z } \\ 26\end{matrix}
root
\sqrt{3}
\sqrt[n]{3}
\sqrt{3}\approx1.732050808\ldots
-b\pm\sqrt{b^2-4\grave{a}c}
Fraction
\frac{2}{4}=0.5
small fraction
\tfrac{2}{4} = 0.5
Large fractions (nested)
\cfrac{2}{c \cfrac{2}{d \cfrac{2}{4}}} =a
Large fractions (not nested)
\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c \dfrac{2}{d \dfrac{2}{4}}} = a
binomial coefficient
\dbinom{n}{r}=\binom{n}{n-r}=C^n_r=C^n_{n-r}
small binomial coefficient
\tbinom{n}{r}=\tbinom{n}{n-r}=C^n_r=C^n_{n-r}
Large binomial coefficient
\binom{n}{r}=\dbinom{n}{n-r}=C^n_r=C^n_{n-r}
array
\begin{array}{|c|c||c|} a & b & S \\ 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}
font
\boldsymbol{a}
Mathematical formula
Sum
\sum_{k=1}^N k^2
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}
Product
\prod_{i=1}^N x_i
\begin{matrix} \prod_{i=1}^N x_i \end{matrix}
Derivative
\mathrm{d}x
upper area
\coprod_{i=1}^N x_i
\begin{matrix} \coprod_{i=1}^N x_i\end{matrix}
limit
\lim_{n \to \infty}x_n
\begin{matrix} \lim_{n \to \infty}x_n\end{matrix}
integral
\int_{-N}^{N} e^x\, dx
\begin{matrix} \int_{-N}^{N} e^x\, dx\end{matrix}
double points
\iint_{D}^{W} \, dx\,dy
triple integral
\iiint_{E}^{V} \, dx\,dy\,dz
Quadruple integral
\iiiint_{F}^{U} \, dx\,dy\,dz\,dt
Closed curve, surface integral
\oint_{C} x^3\, dx 4y^2\, dy
function
\sin \frac{\pi}{3}=\sin 60^ \circ =\frac{\sqrt{3}}{2}
\sin\theta
\arcsin\frac{L}{r}
\cos\theta
\arccos\frac{T}{r}
\tan\theta
\arctan\frac{L}{T}
\sinh g
\operatorname{sh}j
\operatorname{argsh}k
\cosh h
\operatorname{ch}h
\operatorname{argch}l
\tanh i
\operatorname{th}i
\operatorname{argth}m
\lim_{t\to n}T
k'(x)=\lim_{\Delta x\to 0}\frac{k(x)-k(x-\Delta x)}{\Deltax}
\infs
\liminf I
\sup t
\limsup S
\max H
\min L
\exp\!t
\ln
\lgX
1. \log
\log_\alpha X
\ker x
\deg x
\gcd(T,U,V,W,X)
\Pr x
\det x
\hom x
\arg x
\dim x
brackets
brackets
( \frac{1}{2} )
big parantheses
\left( \frac{a}{b} \right)
Solving brackets
\left[ \frac{a}{b} \right]
curly braces
\left\{ \frac{a}{b} \right\}
angle brackets
\left \langle \frac{a}{b} \right \rangle
vertical line
\left| \frac{a}{b} \right|
Another strong line
\left \| \frac{a}{b} \right \|
rounding function
\left \lfloor \frac{a}{b} \right \rfloor
Get the top function
\left \lceil \frac{c}{d} \right \rceil
Slash and backslash
\left / \frac{a}{b} \right \backslash
up and down arrows
\left \uparrow \frac{a}{b} \right \downarrow \left \Uparrow \frac{a}{b} \right \Downarrow \left \updownarrow \frac{a}{b} \right\Updownarrow
mixed brackets
\left [ 0,1 \right ) \left \langle \psi \right |
single bracket
\left \{ \frac{a}{b} \right .
\left . \frac{a}{b} \right \}
matrix
\begin{matrix} x & y \\ z&v \end{matrix}
\begin{vmatrix} x & y \\ z&v \end{vmatrix}
\begin{Vmatrix} x & y \\ z&v \end{Vmatrix}
\begin{Bmatrix} x & y \\ z&v \end{Bmatrix}
\begin{pmatrix} x & y \\ z&v \end{pmatrix}
\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)
equation
\begin{align} \begin{cases} a_2=b_2 1 \\ x=2 y^2 \end{cases} \end{align}
\frac{-b\pm\sqrt{b^2-4\acute{a}c}}{2\acute{a}}
f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n 1, & \mbox{if }n\mbox{ is odd} \end{cases}
\begin{align} f(x) & = (m n)^2 \\ & = m^2 2mn n^2 \\ \end{align}
\begin{alignat}{2} f(x) & = (m-n)^2 \\ f(x) & = (-m n)^2 \\ & = m^2-2mn n^2 \\ \end{alignat}
Multi-line equations (left aligned)
\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x y z \end{array}
\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x y z \end{array}
Multi-line equations (right aligned)
\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x y z \end{array}
Long formula line wrapping
\begin{split} x &= \sqrt {1-y^2}\\ x &= \sqrt[3]{1-y^3} \end{split}
\begin{align} x &= \sqrt {1-y^2}\\ x &= \sqrt[3]{1-y^3} \end{align}
equation set
\begin{cases} 3x 5y z \\ 7x - 2y 4z \\ -6x 3y 2z \end{cases}
\begin{cases} 3x 5y z \\ 7x - 2y 4z \\ -6x 3y 2z \end{cases}
\begin{cases} 3x 5y z \\ 7x - 2y 4z \\ -6x 3y 2z \end{cases}