"행렬과 연립방정식의 수식 표현"의 두 판 사이의 차이

2009년 10월 12일 (월) 18:48 판

$aaa\ldots bbb\cdots ccc\vdots ddd\ddots$

aaa\ldotsbbb\cdotsccc\vdotsddd\ddots

$\mathbf{A} = \begin{bmatrix} 9 & 8 & 6 \\ 1 & 2 & 7 \\ 4 & 9 & 2 \\ 6 & 0 & 5 \end{bmatrix}$

\mathbf{A} = \begin{bmatrix} 9 & 8 & 6 \\ 1 & 2 & 7 \\ 4 & 9 & 2 \\ 6 & 0 & 5 \end{bmatrix}

$\mathbf{A} = \begin{pmatrix} 9 & 8 & 6 \\ 1 & 2 & 7 \\ 4 & 9 & 2 \\ 6 & 0 & 5 \end{pmatrix}$

\mathbf{A} = \begin{pmatrix} 9 & 8 & 6 \\ 1 & 2 & 7 \\ 4 & 9 & 2 \\ 6 & 0 & 5 \end{pmatrix}

$\Large A\ =\ \large\left( \begin{array}{c.cccc}&1&2&\cdots&n\\ \hdash1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)$

\Large A\ =\ \large\left(\begin{array}{c.cccc}&1&2&\cdots&n\\ \hdash1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)

$\begin{alignat}{7} a_{11} x_1 &&\; + \;&& a_{12} x_2 &&\; + \cdots + \;&& a_{1n} x_n &&\; = \;&&& b_1 \\ a_{21} x_1 &&\; + \;&& a_{22} x_2 &&\; + \cdots + \;&& a_{2n} x_n &&\; = \;&&& b_2 \\ \vdots\;\;\; && && \vdots\;\;\; && && \vdots\;\;\; && &&& \;\vdots \\ a_{m1} x_1 &&\; + \;&& a_{m2} x_2 &&\; + \cdots + \;&& a_{mn} x_n &&\; = \;&&& b_m. \\ \end{alignat}$

\begin{alignat}{7} a_{11} x_1 &&\; + \;&& a_{12} x_2 &&\; + \cdots + \;&& a_{1n} x_n &&\; = \;&&& b_1 \\ a_{21} x_1 &&\; + \;&& a_{22} x_2 &&\; + \cdots + \;&& a_{2n} x_n &&\; = \;&&& b_2 \\ \vdots\;\;\; && && \vdots\;\;\; && && \vdots\;\;\; && &&& \;\vdots \\ a_{m1} x_1 &&\; + \;&& a_{m2} x_2 &&\; + \cdots + \;&& a_{mn} x_n &&\; = \;&&& b_m. \\ \end{alignat}

$A= \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix},\quad \bold{x}= \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix},\quad \bold{b}= \begin{bmatrix} b_1 \\ b_2 \\ \vdots \\ b_m \end{bmatrix}$

A= \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix},\quad \bold{x}= \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix},\quad \bold{b}= \begin{bmatrix} b_1 \\ b_2 \\ \vdots \\ b_m \end{bmatrix}

$\mathbf{X}=\left(\begin{array}{ccc}x_{11} & x_{12} & \ldots \\x_{21} & x_{22} & \ldots \\\vdots & \vdots & \ddots\end{array} \right)$

\mathbf{X}=\left(\begin{array}{ccc}x_{11} & x_{12} & \ldots \\x_{21} & x_{22} & \ldots \\\vdots & \vdots & \ddots\end{array} \right)

$\begin{array}{c.cccc}&1&2&\cdots&n\\ \hdash1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}$

\begin{array}{c.cccc}&1&2&\cdots&n\\ \hdash1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}

$\normalsize \left(\large\begin{array}{GC+23} \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\ \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\Large=} \ \left[\begin{array}{CC} \begin{array}\frac1{E_{\fs{+1}x}} &-\frac{\nu_{xy}}{E_{\fs{+1}x}} &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\ -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\ -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}& -\frac{\nu_{zy}}{E_{\fs{+1}z}} &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\ {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\ &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array} \end{array}\right] \ \left(\large\begin{array} \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz} \end{array}\right)$

\normalsize \left(\large\begin{array}{GC+23} \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\ \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\Large=} \ \left[\begin{array}{CC} \begin{array}\frac1{E_{\fs{+1}x}} &-\frac{\nu_{xy}}{E_{\fs{+1}x}} &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\ -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\ -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}& -\frac{\nu_{zy}}{E_{\fs{+1}z}} &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\ {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\ &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array} \end{array}\right] \ \left(\large\begin{array} \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz} \end{array}\right)

$a^2 + b^2 &=& c^2\\ \frac{ab}{2} &=& n$

$\left((x)\right)= \begin{cases} x-\lfloor x\rfloor - 1/2 & \mbox{ if }x\in\mathbb{R}\setminus\mathbb{Z} \\ 0 & \mbox{ if } x\in\mathbb{Z} \end{cases}$

\left((x)\right)= \begin{cases} x-\lfloor x\rfloor - 1/2 & \mbox{ if }x\in\mathbb{R}\setminus\mathbb{Z} \\ 0 & \mbox{ if } x\in\mathbb{Z} \end{cases}

$g_1(\chi) = \begin{cases} \sqrt{p}, & p \equiv 1 \pmod{4}, \\ i \sqrt{p}, & p \equiv 3 \pmod{4}. \end{cases}$

g_1(\chi) = \begin{cases} \sqrt{p}, & p \equiv 1 \pmod{4}, \ i \sqrt{p}, & p \equiv 3 \pmod{4}. \end{cases}

$\left(\frac{a}{p}\right) = \begin{cases} \;\;\,0\mbox{ if } a \equiv 0 \pmod{p} \\+1\mbox{ if }a \not\equiv 0\pmod{p} \mbox{ and for some integer }x, \;a\equiv x^2\pmod{p} \\-1\mbox{ if there is no such } x. \end{cases}$

\left(\frac{a}{p}\right) = \begin{cases} \;\;\,0\mbox{ if } a \equiv 0 \pmod{p} \\+1\mbox{ if }a \not\equiv 0\pmod{p} \mbox{ and for some integer }x, \;a\equiv x^2\pmod{p} \\-1\mbox{ if there is no such } x. \end{cases}

$\tilde y=\left\{ {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right$

\tilde y=\left\{ {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right

$\begin{align} s(x) &= \sum_{k=0}^{\infty} F_k x^k \\ &= F_0 + F_1x + \sum_{k=2}^{\infty} \left( F_{k-1} + F_{k-2} \right) x^k \\ &= x + \sum_{k=2}^{\infty} F_{k-1} x^k + \sum_{k=2}^{\infty} F_{k-2} x^k \\ &= x + x\sum_{k=0}^{\infty} F_k x^k + x^2\sum_{k=0}^{\infty} F_k x^k \\ &= x + x s(x) + x^2 s(x) \end{align}$

\begin{align} s(x) &= \sum_{k=0}^{\infty} F_k x^k \ &= F_0 + F_1x + \sum_{k=2}^{\infty} \left( F_{k-1} + F_{k-2} \right) x^k \ &= x + \sum_{k=2}^{\infty} F_{k-1} x^k + \sum_{k=2}^{\infty} F_{k-2} x^k \ &= x + x\sum_{k=0}^{\infty} F_k x^k + x^2\sum_{k=0}^{\infty} F_k x^k \ &= x + x s(x) + x^2 s(x) \end{align}

$(1) \quad \int_{0}^{\infty} \frac{1}{x^2} dx$

http://en.wikipedia.org/wiki/System_of_linear_equations

2009년 10월 9일 (금) 16:22 판 (원본 보기) http://bomber0.myid.net/ (토론) ← 이전 편집		2009년 10월 12일 (월) 18:48 판 (원본 보기) http://bomber0.myid.net/ (토론) 다음 편집 →
70번째 줄:		70번째 줄:

	# \normalsize \left(\large\begin{array}{GC+23} \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\ \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\Large=} \ \left[\begin{array}{CC} \begin{array}\frac1{E_{\fs{+1}x}} &-\frac{\nu_{xy}}{E_{\fs{+1}x}} &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\ -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\ -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}& -\frac{\nu_{zy}}{E_{\fs{+1}z}} &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\ {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\ &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array} \end{array}\right] \ \left(\large\begin{array} \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz} \end{array}\right)		# \normalsize \left(\large\begin{array}{GC+23} \varepsilon_x\\\varepsilon_y\\\varepsilon_z\\\gamma_{xy}\\ \gamma_{xz}\\\gamma_{yz}\end{array}\right)\ {\Large=} \ \left[\begin{array}{CC} \begin{array}\frac1{E_{\fs{+1}x}} &-\frac{\nu_{xy}}{E_{\fs{+1}x}} &-\frac{\nu_{\fs{+1}xz}}{E_{\fs{+1}x}}\\ -\frac{\nu_{yx}}{E_y}&\frac1{E_{y}}&-\frac{\nu_{yz}}{E_y}\\ -\frac{\nu_{\fs{+1}zx}}{E_{\fs{+1}z}}& -\frac{\nu_{zy}}{E_{\fs{+1}z}} &\frac1{E_{\fs{+1}z}}\end{array} & {\LARGE 0} \\ {\LARGE 0} & \begin{array}\frac1{G_{xy}}&&\\ &\frac1{G_{\fs{+1}xz}}&\\&&\frac1{G_{yz}}\end{array} \end{array}\right] \ \left(\large\begin{array} \sigma_x\\\sigma_y\\\sigma_z\\\tau_{xy}\\\tau_{xz}\\\tau_{yz} \end{array}\right)
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		+	<math>a^2 + b^2 &=& c^2\\ \frac{ab}{2} &=& n</math>
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"행렬과 연립방정식의 수식 표현"의 두 판 사이의 차이

2009년 10월 12일 (월) 18:48 판

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