# 行向量與列向量

m-by-n matrix」的各地常用別名

「横排（row）」的各地常用別名

「纵排（column）」的各地常用別名

${\displaystyle \mathbf {x} ={\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}\,}$

${\displaystyle \mathbf {x} ={\begin{bmatrix}x_{1}&x_{2}&\dots &x_{m}\end{bmatrix}}\,}$

${\displaystyle {\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}^{\rm {T}}={\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}\,}$

${\displaystyle {\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}^{\rm {T}}={\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}\,}$

## 標示

${\displaystyle \mathbf {x} ={\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}^{\rm {T}}}$

${\displaystyle \mathbf {x} ={\begin{bmatrix}x_{1},x_{2},\dots ,x_{m}\end{bmatrix}}^{\rm {T}}}$

${\displaystyle {\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}}$ ${\displaystyle {\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}{\text{ 或 }}{\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}^{\rm {T}}}$
Alternative notation 1
(commas, transpose signs)
${\displaystyle {\begin{bmatrix}x_{1},x_{2},\dots ,x_{m}\end{bmatrix}}}$ ${\displaystyle {\begin{bmatrix}x_{1},x_{2},\dots ,x_{m}\end{bmatrix}}^{\rm {T}}}$
Alternative notation 2
(commas and semicolons, no transpose sign
${\displaystyle {\begin{bmatrix}x_{1},x_{2},\dots ,x_{m}\end{bmatrix}}}$ ${\displaystyle {\begin{bmatrix}x_{1};x_{2};\dots ;x_{m}\end{bmatrix}}}$

## 操作

${\displaystyle \mathbf {a} \cdot \mathbf {b} =\mathbf {a} ^{\mathrm {T} }\mathbf {b} ={\begin{bmatrix}a_{1}&a_{2}&a_{3}\end{bmatrix}}\ {\begin{bmatrix}b_{1}\\b_{2}\\b_{3}\end{bmatrix}}=a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}\ }$

${\displaystyle \mathbf {b} \cdot \mathbf {a} =\mathbf {b} ^{\mathrm {T} }\mathbf {a} ={\begin{bmatrix}b_{1}&b_{2}&b_{3}\end{bmatrix}}\ {\begin{bmatrix}a_{1}\\a_{2}\\a_{3}\end{bmatrix}}\ }$

${\displaystyle \mathbf {a} \otimes \mathbf {b} =\mathbf {a} \mathbf {b} ^{\mathrm {T} }={\begin{bmatrix}a_{1}\\a_{2}\\a_{3}\end{bmatrix}}\ {\begin{bmatrix}b_{1}&b_{2}&b_{3}\end{bmatrix}}={\begin{bmatrix}a_{1}b_{1}&a_{1}b_{2}&a_{1}b_{3}\\a_{2}b_{1}&a_{2}b_{2}&a_{2}b_{3}\\a_{3}b_{1}&a_{3}b_{2}&a_{3}b_{3}\\\end{bmatrix}}\ }$

${\displaystyle \mathbf {b} \otimes \mathbf {a} =\mathbf {b} \mathbf {a} ^{\mathrm {T} }={\begin{bmatrix}b_{1}\\b_{2}\\b_{3}\end{bmatrix}}\ {\begin{bmatrix}a_{1}&a_{2}&a_{3}\end{bmatrix}}={\begin{bmatrix}b_{1}a_{1}&b_{1}a_{2}&b_{1}a_{3}\\b_{2}a_{1}&b_{2}a_{2}&b_{2}a_{3}\\b_{3}a_{1}&b_{3}a_{2}&b_{3}a_{3}\\\end{bmatrix}}\ }$

## 优选输入的向量矩阵变换

${\displaystyle vM=p\ }$

${\displaystyle pQ=t\ }$

${\displaystyle p=Mv\,,\quad t=Qp}$

${\displaystyle \alpha (ST)=(\alpha S)T=\beta T=\gamma }$中。 」

(希腊字母代表行向量)。

## 参考文献

1. ^ Meyer (2000), p. 8
2. ^ Raiz A. Usmani (1987) Applied Linear Algebra Marcel Dekker ISBN 0824776224.
• Axler, Sheldon Jay, Linear Algebra Done Right 2nd, Springer-Verlag, 1997, ISBN 0-387-98259-0
• Lay, David C., Linear Algebra and Its Applications 3rd, Addison Wesley, August 22, 2005, ISBN 978-0-321-28713-7
• Meyer, Carl D., Matrix Analysis and Applied Linear Algebra, Society for Industrial and Applied Mathematics (SIAM), February 15, 2001 [2017年5月13日], ISBN 978-0-89871-454-8, （原始内容存档于2001年3月1日）
• Poole, David, Linear Algebra: A Modern Introduction 2nd, Brooks/Cole, 2006, ISBN 0-534-99845-3
• Anton, Howard, Elementary Linear Algebra (Applications Version) 9th, Wiley International, 2005
• Leon, Steven J., Linear Algebra With Applications 7th, Pearson Prentice Hall, 2006