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
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
\frac{a}{b} % Standard fraction
\sqrt{x} % Square root
\sqrt[n]{x} % n-th root
\binom{n}{k} % Binomial coefficient
Examples:
$$
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}
$$
$$
\sqrt{a^2 + b^2} = c \qquad \sqrt[3]{27} = 3
$$
3. Superscripts and Subscripts
$x^2$ % 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
$$
A = \begin{pmatrix}
a & b \\
c & d
\end{pmatrix}
$$
$$
\det(A) = \begin{vmatrix}
a & b \\
c & d
\end{vmatrix} = ad - bc
$$
$$
I = \begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
$$
With Ellipsis
$$
\begin{pmatrix}
a_{11} & \cdots & a_{1n} \\
\vdots & \ddots & \vdots \\
a_{m1} & \cdots & a_{mn}
\end{pmatrix}
$$
7. Aligned Equations
Use aligned environment with & for alignment and \\ for line breaks:
$$
\begin{aligned}
(a+b)^2 &= (a+b)(a+b) \\
&= a^2 + 2ab + b^2
\end{aligned}
$$
Conditional Definitions (cases)
$$
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x & \text{if } x < 0
\end{cases}
$$
Text in Math
Use \text{...} for regular text:
$$
x = 5 \text{ where } x \in \mathbb{N}
$$
8. Integrals, Sums, and Limits
Integrals
$$
\int_a^b f(x) \, dx \qquad \iint_D f \, dA \qquad \oint_C \mathbf{F} \cdot d\mathbf{r}
$$
Tip: Use \, before dx for proper spacing.
Sums and Products
$$
\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}
$$
$$
\prod_{i=1}^{n} a_i
$$
Limits
$$
\lim_{x \to 0} \frac{\sin x}{x} = 1
$$
$$
\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e
$$
9. Delimiters
Use \left and \right for auto-sizing:
$$
\left( \frac{a}{b} \right) \qquad \left[ \sum_{i=1}^{n} x_i \right] \qquad \left\{ x : x > 0 \right\}
$$
One-sided Delimiter
Use \left. or \right. for invisible delimiter:
$$
\left. \frac{df}{dx} \right|_{x=0}
$$
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
$$
\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}
$$
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
$$
\overbrace{a + b + c}^{\text{sum}} = \underbrace{x + y + z}_{\text{total}}
$$
Arrows
$$
\overrightarrow{AB} \qquad \overleftarrow{CD}
$$
12. Common Patterns
Derivatives
$$
\frac{dy}{dx} \qquad \frac{\partial f}{\partial x} \qquad \nabla f
$$
Norm and Absolute Value
$$
\|x\| = \sqrt{\sum x_i^2} \qquad |x - y| \leq |x| + |y|
$$
Probability
$$
P(A \mid B) = \frac{P(B \mid A) P(A)}{P(B)}
$$
$$
\mathbb{E}[X] = \sum_{i} x_i P(X = x_i)
$$
Quick Reference
% 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}