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}