まくまくOctaveノート
TeX メモ
2017-03-24

記号

TeX 表示 説明
{}^t\!A \({}^t\!A\) 転置行列
A^{\mathrm{T}} \(A^{\mathrm{T}}\) 転置行列

行列

\[A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}\]
A = \begin{bmatrix}
  1 & 2 \\
  3 & 4 \\
  5 & 6
\end{bmatrix}

あるいは、

A = \left[
  \begin{array}{cc}
    1 & 2 \\
    3 & 4 \\
    5 & 6
  \end{array}
\right]

行列の各要素を右寄せ

\[A = \left[ \begin{array}{rrr} 134 & 30 & 7 \\ -44 & -2 & 1000 \\ 3 & 9 & -7 \end{array} \right]\]
a = \left[
  \begin{array}{rrr}
    134 & 30 & 7 \\
    -44 & -2 & 1000 \\
    3 & 9 & -7
  \end{array}
\right]

括弧なしの行列

\[\begin{matrix} a & b \\ c & d \end{matrix}\]
\begin{matrix}
  a & b \\
  c & d
\end{matrix}

ドットで要素を省略

\[A = \begin{pmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \ldots & a_{mn} \end{pmatrix}\]
A = \begin{pmatrix}
  a_{11} & a_{12} & \ldots & a_{1n} \\
  a_{21} & a_{22} & \ldots & a_{2n} \\
  \vdots & \vdots & \ddots & \vdots \\
  a_{m1} & a_{m2} & \ldots & a_{mn}
\end{pmatrix}

逆行列

\[\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^{-1} = \begin{bmatrix} -2 & 1 \\ 1.5 & -0.5 \end{bmatrix}\]
\begin{bmatrix}
  1 & 2 \\
  3 & 4
\end{bmatrix}^{-1} =
\begin{bmatrix}
  -2 & 1 \\
  1.5 & -0.5
\end{bmatrix}

行列式

\[\mathrm{det}A = |A| = \left| \begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array} \right|\]
\mathrm{det}A = |A| = \left|
  \begin{array}{ccc}
    a_{11} & a_{12} & a_{13} \\
    a_{21} & a_{22} & a_{23} \\
    a_{31} & a_{32} & a_{33}
  \end{array}
\right|

場合分け

\[x^n = \left\{ \begin{array}{ll} 1 & (n=0) \\ x \cdot x^{n-1} & (otherwise) \end{array} \right.\]
x^n = \left\{ \begin{array}{ll}
  1 & (n=0) \\
  x \cdot x^{n-1} & (otherwise)
\end{array} \right.

その他

\[\begin{align*} \frac{\partial \theta}{\partial t}= \frac{\partial}{\partial z} \left[ K(\theta) \left (\frac{\partial \psi}{\partial z} + 1 \right) \right]\ \end{align*}\]
2017-03-24