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This is a test post to demonstrate LaTeX equation support using KaTeX.

Inline Equations

Here’s Einstein’s famous equation: $E = mc^2$

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The integral of a Gaussian function:

\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}

Maxwell’s equations in differential form:

\begin{align} \nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0} \\ \nabla \cdot \vec{B} &= 0 \\ \nabla \times \vec{E} &= -\frac{\partial \vec{B}}{\partial t} \\ \nabla \times \vec{B} &= \mu_0\vec{J} + \mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t} \end{align}

\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} ax + by \\ cx + dy \end{bmatrix}

LaTeX rendering is working perfectly! This blog is ready for technical writing with beautiful mathematical equations.