$$ as inline mathmatics, add the following code in _includes/head.html: <!-- Mathjax Support -->
<script>
MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']]
}
};
</script>
<script id="MathJax-script" async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js">
</script>
inlineMath is used to define the inline math delimiter. It is to enable $$ can be used in kramdown for inline mathmatical formula.
Math syntax in kramdown: the default math delimiters are $$...$$ and \[...\] for displayed mathematics, and \(...\) for in-line mathematics.
\\ as \ by default in markdown parser. And \ is an escape character commonly used across many programming languages. You could use a \ before every actual \ you want to use. So if you wanted \begin{bmatrix} you would have to write \\begin{bmatrix} and if you want \\ you need to use \\\\. $ \\begin{bmatrix}a & b \\\\ c & d\\end{bmatrix} $
| To avoid | in $$ part. But use \vert !!! |
$$
\\begin{align*}
& \phi(x,y) = \phi \left(\sum_{i=1}^n x_ie_i, \sum_{j=1}^n y_je_j \right)
= \sum_{i=1}^n \sum_{j=1}^n x_i y_j \phi(e_i, e_j) = \\
& (x_1, \ldots, x_n) \left( \\begin{array}{ccc}
\phi(e_1, e_1) & \cdots & \phi(e_1, e_n) \\
\vdots & \ddots & \vdots \\
\phi(e_n, e_1) & \cdots & \phi(e_n, e_n)
\end{array} \right)
\left( \\begin{array}{c}
y_1 \\
\vdots \\
y_n
\end{array} \right)
\end{align*}
$$