40 lines
1,017 B
Markdown
40 lines
1,017 B
Markdown
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---
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title: "Test Tex"
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date: 2022-08-26T22:28:10+08:00
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mathjax: true
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draft: true
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---
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Inline math: {{< texi `\varphi` >}}
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Displayed math:
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{{< texd `\begin{aligned}
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\varphi &\Rightarrow \psi \\
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\varnothing &\rightarrow A
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\end{aligned}` >}}
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$$
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R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda
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= {8 \pi G \over c^4} T_{\mu \nu}
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$$
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The equation $$(x_i \cdot x_j)^2$$ is called kernel function and is often written as $$k(x_i, x_j)$$.
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$$
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\arg\max_\alpha \sum_j \alpha_j - \frac{1}{2} \sum_{j,k} \alpha_j, \alpha_k y_j y_k (x_j \cdot x_k)
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$$
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$$
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f(X) = \frac{1}{(2\pi)^{\frac{n}{2} |\Sigma|^{\frac{1}{2}}}} e^{ - \frac{1}{2} (X - \mu)^T \Sigma^{-1} (X - \mu)}
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$$
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$$
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\mu_i = \sum_{j=1}^N \frac{p_{ij} x}{n_i} \\
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\Sigma_i = \sum_{j=1}^N \frac{p_{ij} (x_j - \mu_i) (x_j - \mu_i)^T}{n_i}\\
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w_i = \frac{n_i}{N}
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$$
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$$
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S_i^{(t)} = \big \{ x_p : \big \| x_p - \mu^{(t)}_i \big \|^2 \le \big \| x_p - \mu^{(t)}_j \big \|^2 \ \forall j, 1 \le j \le k \big\}
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$$
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(The error above is a demo for incorrect formulas.)
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