LaTeX Math & Equations in Markdown Tables

In Markdown processing pipelines (such as GitHub Flavored Markdown, Hugo, and Obsidian),the table parser executes first, scanning for the | character to construct the grid. Only after the table cells are isolated does the math engine (KaTeX or MathJax) render formulas inside the cells. If you type $|x|$, the table parser sees the first pipe as the end of the cell, destroying column boundaries:

| Loss Function | Mathematical Formulation | Optimization Target |
| :------------ | :----------------------- | :------------------ |
| L1 Loss (MAE) | $\mathcal{L} = \frac{1}{n} \sum \lvert y_i - \hat{y}_i \rvert$ | Robust to outliers |
| L2 Loss (MSE) | $\mathcal{L} = \frac{1}{n} \sum (y_i - \hat{y}_i)^2$ | Penalizes large errors |
| Huber Loss    | $\begin{cases} \frac{1}{2}(y - \hat{y})^2 & \text{for } \lvert y - \hat{y} \rvert \le \delta \\ \delta(\lvert y - \hat{y} \rvert - \frac{1}{2}\delta) & \text{otherwise} \end{cases}$ | Smooth transition |

Never use display math blocks ($$ ... $$) inside Markdown table cells. Display math creates block-level container boundaries that break GFM row continuity. Instead, use inline single dollar signs ($...$) paired with \dfrac or compact notation:

| Metric | Formula |
| :--- | :--- |
| Mean | $$ \mu = \frac{\sum x}{n} $$ |

| Metric | Formula |
| :--- | :--- |
| Mean | $\mu = \frac{1}{n} \sum x_i$ |

You can embed transformation matrices and linear algebra vectors inside table cells using the standard \begin{pmatrix} environment. Because LaTeX interprets \\\\ as an internal matrix row separator, it does not conflict with Markdown table lines:

| Operation | 2D Transformation Matrix | Determinant |
| :-------- | :----------------------- | :---------- |
| Rotation ($	heta$) | $\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$ | $\det(R) = 1$ |
| Scaling ($s_x, s_y$) | $\begin{pmatrix} s_x & 0 \\ 0 & s_y \end{pmatrix}$ | $\det(S) = s_x s_y$ |