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name: mathjax-rendering description: Render mathematical formulas in Obsidian using LaTeX/MathJax syntax. Use when writing equations, matrices, integrals, summations, or any mathematical notation in Obsidian notes.

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

CopyInline: 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

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2. Fractions and Roots

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

Examples:

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

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

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3. Superscripts and Subscripts

Copy$x^2$           % 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.

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4. Greek Letters

Common Letters

See reference.md for complete Greek alphabet.

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5. Common Operators and Symbols

See reference.md for complete symbol tables.

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6. Matrices

Matrix Environments

Examples

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

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

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

With Ellipsis

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

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7. Aligned Equations

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

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

Conditional Definitions (cases)

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

Text in Math

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

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

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8. Integrals, Sums, and Limits

Integrals

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

Tip: Use \, before dx for proper spacing.

Sums and Products

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

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

Limits

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

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

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9. Delimiters

Use \left and \right for auto-sizing:

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

One-sided Delimiter

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

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

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10. Font Styles

Number Sets

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

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11. Decorations

Overbrace/Underbrace

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

Arrows

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

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12. Common Patterns

Derivatives

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

Norm and Absolute Value

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

Probability

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

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

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Quick Reference

Copy% 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}