MathJax Rendering in Obsidian

Obsidian uses MathJax to render LaTeX math expressions. This skill covers essential syntax for mathematical notation.

For complete symbol tables and advanced commands, see reference.md.

1. Basic Syntax

Inline vs Block

markdown

Inline: The equation $E = mc^2$ appears within text.

Block (centered, display-style):
$$
\int_0^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}
$$

•Inline ( $...$ ): Compact, flows with paragraph
•Block ($$...$$): Larger, centered, multi-line capable

2. Fractions and Roots

latex

\frac{a}{b}       % Standard fraction
\sqrt{x}          % Square root
\sqrt[n]{x}       % n-th root
\binom{n}{k}      % Binomial coefficient

Examples:

latex

$$
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}
$$

$$
\sqrt{a^2 + b^2} = c \qquad \sqrt[3]{27} = 3
$$

3. Superscripts and Subscripts

latex

$x^2$           % Superscript
$x_1$           % Subscript
$x_i^2$         % Both combined
$x^{10}$        % Multiple characters need braces
$x_{n+1}$       % Expression as subscript

Note: Use braces {} for multi-character exponents/subscripts.

4. Greek Letters

Common Letters

Lowercase		Uppercase
`\alpha` α	`\beta` β	`\Gamma` Γ	`\Delta` Δ
`\gamma` γ	`\delta` δ	`\Theta` Θ	`\Lambda` Λ
`\epsilon` ε	`\theta` θ	`\Sigma` Σ	`\Phi` Φ
`\lambda` λ	`\mu` μ	`\Psi` Ψ	`\Omega` Ω
`\pi` π	`\sigma` σ
`\phi` φ	`\omega` ω

See reference.md for complete Greek alphabet.

5. Common Operators and Symbols

Symbol	Syntax	Symbol	Syntax
≤	`\leq`	∈	`\in`
≥	`\geq`	∉	`\notin`
≠	`\neq`	⊂	`\subset`
≈	`\approx`	∪	`\cup`
×	`\times`	∩	`\cap`
·	`\cdot`	∞	`\infty`
±	`\pm`	∂	`\partial`
∀	`\forall`	∇	`\nabla`
∃	`\exists`	∅	`\emptyset`

See reference.md for complete symbol tables.

6. Matrices

Matrix Environments

Environment	Brackets
`pmatrix`	( )
`bmatrix`	[ ]
`vmatrix`	\| \| (determinant)
`Bmatrix`	{ }

Examples

latex

$$
A = \begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
$$

$$
\det(A) = \begin{vmatrix}
a & b \\
c & d
\end{vmatrix} = ad - bc
$$

$$
I = \begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
$$

With Ellipsis

latex

$$
\begin{pmatrix}
a_{11} & \cdots & a_{1n} \\
\vdots & \ddots & \vdots \\
a_{m1} & \cdots & a_{mn}
\end{pmatrix}
$$

7. Aligned Equations

Use aligned environment with & for alignment and \\ for line breaks:

latex

$$
\begin{aligned}
(a+b)^2 &= (a+b)(a+b) \\
        &= a^2 + 2ab + b^2
\end{aligned}
$$

Conditional Definitions (cases)

latex

$$
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x  & \text{if } x < 0
\end{cases}
$$

Text in Math

Use \text{...} for regular text:

latex

$$
x = 5 \text{ where } x \in \mathbb{N}
$$

8. Integrals, Sums, and Limits

Integrals

latex

$$
\int_a^b f(x) \, dx \qquad \iint_D f \, dA \qquad \oint_C \mathbf{F} \cdot d\mathbf{r}
$$

Tip: Use \, before dx for proper spacing.

Sums and Products

latex

$$
\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}
$$

$$
\prod_{i=1}^{n} a_i
$$

Limits

latex

$$
\lim_{x \to 0} \frac{\sin x}{x} = 1
$$

$$
\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e
$$

9. Delimiters

Use \left and \right for auto-sizing:

latex

$$
\left( \frac{a}{b} \right) \qquad \left[ \sum_{i=1}^{n} x_i \right] \qquad \left\{ x : x > 0 \right\}
$$

One-sided Delimiter

Use \left. or \right. for invisible delimiter:

latex

$$
\left. \frac{df}{dx} \right|_{x=0}
$$

10. Font Styles

Style	Syntax	Use Case
Bold	`\mathbf{v}`	Vectors
Roman	`\mathrm{d}x`	Differential d
Blackboard	`\mathbb{R}`	Number sets
Calligraphic	`\mathcal{L}`	Operators

Number Sets

latex

$$
\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}
$$

11. Decorations

Decoration	Syntax
Hat	`\hat{x}`
Bar	`\bar{x}`
Tilde	`\tilde{x}`
Vector	`\vec{x}`
Dot	`\dot{x}`
Double dot	`\ddot{x}`

Overbrace/Underbrace

latex

$$
\overbrace{a + b + c}^{\text{sum}} = \underbrace{x + y + z}_{\text{total}}
$$

Arrows

latex

$$
\overrightarrow{AB} \qquad \overleftarrow{CD}
$$

12. Common Patterns

Derivatives

latex

$$
\frac{dy}{dx} \qquad \frac{\partial f}{\partial x} \qquad \nabla f
$$

Norm and Absolute Value

latex

$$
\|x\| = \sqrt{\sum x_i^2} \qquad |x - y| \leq |x| + |y|
$$

Probability

latex

$$
P(A \mid B) = \frac{P(B \mid A) P(A)}{P(B)}
$$

$$
\mathbb{E}[X] = \sum_{i} x_i P(X = x_i)
$$

Quick Reference

latex

% Fractions and roots
\frac{a}{b}  \sqrt{x}  \sqrt[n]{x}

% Greek (common)
\alpha \beta \gamma \theta \lambda \pi \sigma \omega
\Gamma \Delta \Sigma \Omega

% Relations
= \neq \leq \geq \approx \equiv \in \subset

% Operations
+ - \times \div \cdot \pm

% Calculus
\int \sum \prod \lim \partial \nabla

% Sets
\mathbb{R} \mathbb{N} \mathbb{Z} \mathbb{Q} \mathbb{C}

% Decorations
\hat{x} \bar{x} \vec{x} \dot{x}