Mathematical operators
Dot product (Inner product)
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| \langle\boldsymbol{u},\boldsymbol{v}\rangle=\boldsymbol{u}^T\boldsymbol{v}
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Note that, the appearance of inputing < and > directly is very different from that using \langle and \rangle:
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| <\boldsymbol{u},\boldsymbol{v}>=\boldsymbol{u}^T\boldsymbol{v}
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Cross product (Vector product)
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| \boldsymbol{u}\times\boldsymbol{v}
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Or using wedge notation \wedge :
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| \boldsymbol{u}\wedge\boldsymbol{v}
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Kronecker product (Tensor product, Outer product) and other similar operators
Kronecker product (or tensor product):
\[A\otimes B\notag\]
or denote outer product of vectors:
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| \boldsymbol{u}\otimes\boldsymbol{v}^T
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and some other similar symbols :
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| \oplus, \ominus, \odot, \oslash, \bigotimes, \bigoplus, \bigodot
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Combination symbol
\[{n \choose k}\notag\]
Mathematical symbols
“For all” and “Exist” symbol
\[\forall, \exists\notag\]
Function mapping symbol
\[\mapsto\notag\]
Matrix environments
matrix environment
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| \begin{matrix}
a&b&c\\
d&e&f\\
g&h&i\\
\end{matrix}
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bmatrix environment
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| \begin{bmatrix}
a&b&c\\
d&e&f\\
g&h&i\\
\end{bmatrix}
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vmatrix environment
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| \begin{vmatrix}
a&b&c\\
d&e&f\\
g&h&i\\
\end{vmatrix}
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pmatrix environment
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| \begin{pmatrix}
a&b&c\\
d&e&f\\
g&h&i\\
\end{pmatrix}
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Bmatrix envrionment
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| \begin{Bmatrix}
a&b&c\\
d&e&f\\
g&h&i\\
\end{Bmatrix}
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Vmatrix environment
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| \begin{Vmatrix}
a&b&c\\
d&e&f\\
g&h&i\\
\end{Vmatrix}
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Block matrix
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| \begin{pmatrix}
\begin{matrix}
1&0\\
0&1\\
\end{matrix}&0\\
0&\begin{matrix}
1&0\\
0&-1\\
\end{matrix}
\end{pmatrix}
|
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| \begin{bmatrix}
\begin{pmatrix}
1&0\\
0&1\\
\end{pmatrix}&0\\
0&\begin{pmatrix}
1&0\\
0&-1\\
\end{pmatrix}
\end{bmatrix}
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bordermatrix environment
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| \begin{equation}
\bordermatrix{
& 1 & 2 & 3 \cr
1 & A & B & C \cr
2 & D & E & F \cr}
\end{equation}
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Note that here, bordermatrix environment is not available in Markdown MathJax.
References