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LinearAlgebra.md

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线性代数(Linear Algebra)

$ { , _ \

$$ \backslash $$

$$ \alpha, \beta, …, \omega $$

$$ \Gamma, \Delta, …, \Omega $$

$$ \land, \lor, \lnot, \forall, \exists, \top, \bot, \vdash, \vDash $$

$$ \lt, \gt, \le, \ge, \neq, \not, \not\lt $$

$$ \times, \div, \pm, \mp, \cdot $$

$$ \cup, \cap, \setminus, \subset, \subseteq, \subsetneq, \supset, \in, \notin, \emptyset, \varnothing $$

$$ \to, \rightarrow, \leftarrow, \Rightarrow, \Leftarrow, \mapsto $$

$$ \star, \ast, \oplus, \circ, \bullet $$

$$ \approx, \sim, \simeq, \cong, \equiv, \prec, \lhd $$

$$ \infty, \aleph_0, \nabla, \partial, \Im, \Re $$

$$ a\equiv b\pmod n $$

$$ \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6} $$

$$ \lim_{x\to 0} f(x) $$

$$ \binom{n+1}{2k} $$

$$ a, b, \ldots , y, z $$

$$ a + b + \cdots + y + z $$

$$ \begin{pmatrix} 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \end{pmatrix} $$

$$ \begin{bmatrix} 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \end{bmatrix} $$

$$ \begin{Bmatrix} 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \end{Bmatrix} $$

$$ \begin{vmatrix} 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \end{vmatrix} $$

$$ \begin{Vmatrix} 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \\ 1 & 2 & 3 & 4 \end{Vmatrix} $$

$$ \begin{pmatrix} 1 & a_1 & a_1^2 & \cdots & a_1^n \\ 1 & a_2 & a_2^2 & \cdots & a_2^n \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & a_m & a_m^2 & \cdots & a_m^n \end{pmatrix} $$

$$ \epsilon, \varepsilon, \phi, \varphi, \ell $$

$$ \prod, \bigcup, \bigcap, \int, \iint, \iiint $$

$$ a, b, a; b, a\quad b, a\qquad b $$

$$ \hat x, \widehat {abc}, \bar x, \overline {abc}, \vec x, \overrightarrow {abc}, \overleftrightarrow {abc}, \dot x \ddot x $$

$$ \text{is extra large} $$

$$ x^{y^z} $$

$$ {a+1\over b+1} $$

$$ \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) $$

$$ \left(\frac{\sqrt x}{y^3}\right) $$

$$ \begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \end{matrix} $$

$$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array} $$

$$ \mathbf {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$ \mathtt {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$ \mathrm {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$ \mathsf {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$ \mathcal {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$ \mathscr {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$ \mathfrak {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$ \mathbb {ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz} $$

$$a{\bold e}\alpha + b\tilde{\bold e}\alpha + c{\bold e}_x = \bold 0$$

$${\bold e}\alpha = \begin{pmatrix}\cos\alpha\ \sin\alpha\end{pmatrix} \quad and \quad {\tilde\bold e}\alpha = \begin{pmatrix}-\sin\alpha\ \cos\alpha\end{pmatrix}$$

$$-c{\bold e}x = a{\bold e}\alpha + b\tilde{\bold e}_\alpha$$

$$c^2 = a^2 + b^2$$ (2)

$cp = a^2$

$cq = b^2$

$pq = h^2$