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\begin_body

\begin_layout Title
术语表
\end_layout

\begin_layout Description
乘法的结合律 
\begin_inset Formula $A(BC)=(AB)C$
\end_inset

, 对所有 
\begin_inset Formula $A,B,C$
\end_inset

 均成立.
 
\end_layout

\begin_layout Description
系数矩阵 一个矩阵, 它的元素是一个线性方程组的系数.
 
\end_layout

\begin_layout Description
余子式 一个数 
\begin_inset Formula $C_{ij}=(-1)^{i+j}\mathrm{det}A_{ij}$
\end_inset

, 称为矩阵 
\begin_inset Formula $A(i,j)$
\end_inset

 元素的余子式, 此处 
\begin_inset Formula $A_{ij}$
\end_inset

 是划去 
\begin_inset Formula $A$
\end_inset

 中 
\begin_inset Formula $i$
\end_inset

 行和 
\begin_inset Formula $j$
\end_inset

 列后构成的子矩阵.
\end_layout

\begin_layout Description
伴随矩阵 矩阵 
\begin_inset Formula $A^{*}$
\end_inset

 是方阵 
\begin_inset Formula $A$
\end_inset

 中 
\begin_inset Formula $(i,j)$
\end_inset

 位置的元素, 用 
\begin_inset Formula $A$
\end_inset

 中 
\begin_inset Formula $(i,j)$
\end_inset

 元素的代数余子式代替后，再通过转置得到的矩阵.
\end_layout

\begin_layout Description
分块矩阵 见矩阵分划.
 
\end_layout

\begin_layout Description
分块矩阵乘法 分块后矩阵的行列乘法, 将块作为数来对待.
 
\end_layout

\begin_layout Description
上三角形分块矩阵 分块矩阵 
\begin_inset Formula $A=\left[A_{ij}\right]$
\end_inset

, 使得一块 
\begin_inset Formula $A_{ij}$
\end_inset

 对 
\begin_inset Formula $i>j$
\end_inset

 是零分块.
 
\end_layout

\begin_layout Description
分块对角矩阵 一个分块矩阵 
\begin_inset Formula $A=\left[A_{ij}\right]$
\end_inset

, 使得 
\begin_inset Formula $i\neq j$
\end_inset

 时, 每一块 
\begin_inset Formula $A_{ij}$
\end_inset

 是零矩阵.
\end_layout

\begin_layout Description
非零向量之间的夹角 夹角 
\begin_inset Formula $\vartheta$
\end_inset

 是指从原点到点 
\begin_inset Formula $\boldsymbol{u}$
\end_inset

 和 
\begin_inset Formula $\boldsymbol{v}$
\end_inset

 的两个线段之间的角度，通过点积联系起来。 
\begin_inset Formula 
\[
\boldsymbol{u}\cdot\boldsymbol{v}=\|\boldsymbol{u}\|\|\boldsymbol{v}\|\cos\vartheta.
\]

\end_inset


\end_layout

\begin_layout Description
柯西-施瓦茨不等式 对所有 
\begin_inset Formula $\boldsymbol{u},\boldsymbol{v}$
\end_inset

 有 
\begin_inset Formula $|\langle\boldsymbol{u},\boldsymbol{v}\rangle|\leqslant\|\boldsymbol{u}\|\cdot\|\boldsymbol{v}\|$
\end_inset

.
 
\end_layout

\begin_layout Description
向量空间中的一个非平凡子空间的基 一 个 
\begin_inset Formula $V$
\end_inset

 中的向量集 
\begin_inset Formula $\mathcal{B}=\left\{ \boldsymbol{v}_{1},\cdots,\boldsymbol{v}_{p}\right\} $
\end_inset

, 使得 
\begin_inset Newline newline
\end_inset

(i) 
\begin_inset Formula $\mathcal{B}$
\end_inset

 是线性无关集，
\begin_inset Newline newline
\end_inset

(ii) 由 
\begin_inset Formula $\mathcal{B}$
\end_inset

 生成的子空间和 
\begin_inset Formula $H$
\end_inset

 一致, 即 
\begin_inset Formula $H=\mathrm{Span}\left\{ \boldsymbol{v}_{1},\cdots,\boldsymbol{v}_{p}\right\} $
\end_inset

.
 
\begin_inset Formula $\mathcal{B}$
\end_inset

-coordinates of 
\begin_inset Formula $x$
\end_inset

, (
\begin_inset Formula $x$
\end_inset

 的 
\begin_inset Formula $\mathcal{B}$
\end_inset

 坐标) 即 
\begin_inset Formula $x$
\end_inset

 相对于基 
\begin_inset Formula $\mathcal{B}$
\end_inset

 的坐标.
 
\end_layout

\begin_layout Description
基本变量 线性方程组中对应系数矩阵主元列的变量.
 
\end_layout

\begin_layout Description
增广矩阵 一个由线性方程组的系数矩阵和右边增加一列或多列构成的矩阵, 每一个增加的列包含给定系数矩阵对应方程组右边的常数项.
 
\end_layout

\begin_layout Description
代数重数 一个特征值的重数是作为特征方程的根的重数.
 
\end_layout

\begin_layout Description
\begin_inset Formula $A$
\end_inset

的特征方程 
\begin_inset Formula $\mathrm{det}(A-\lambda I)=0$
\end_inset

.
 
\end_layout

\begin_layout Description
\begin_inset Formula $A$
\end_inset

的特征多项式 
\begin_inset Formula $\mathrm{det}(A-\lambda I)$
\end_inset

 或在有些教材中, 
\begin_inset Formula $\mathrm{det}(\lambda I-A)$
\end_inset

.
 
\end_layout

\begin_layout Description
基的变换 见矩阵坐标变换.
 
\end_layout

\begin_layout Description
从一个基
\begin_inset Formula $\mathcal{B}$
\end_inset

到一个基
\begin_inset Formula $\mathcal{C}$
\end_inset

的矩阵坐标变换 一个矩阵 
\begin_inset Formula $\underset{\mathcal{C}\leftarrow\mathcal{B}}{P}$
\end_inset

 将 
\begin_inset Formula $\mathcal{B}$
\end_inset

 坐标向量变换为 
\begin_inset Formula $\mathcal{C}$
\end_inset

 坐标向量, 
\begin_inset Formula $[\boldsymbol{x}]_{\mathcal{C}}=\underset{\mathcal{C}\leftarrow\mathcal{B}}{P}[\boldsymbol{x}]_{\mathcal{B}}$
\end_inset

, 如果 
\begin_inset Formula $\mathcal{C}$
\end_inset

 是 
\begin_inset Formula $\mathbb{R}^{n}$
\end_inset

 中的标准基, 那么有时也将 
\begin_inset Formula $\underset{\mathcal{C}\leftarrow\mathcal{B}}{P}$
\end_inset

 记作 
\begin_inset Formula $P_{\mathcal{B}}$
\end_inset

.
 
\end_layout

\begin_layout Description
楚列斯基分解 一个分解 
\begin_inset Formula $A=R^{\mathrm{T}}R$
\end_inset

, 此处 
\begin_inset Formula $R$
\end_inset

 是一个可逆上三角形矩阵, 它的所有对角元素为正的.
 
\end_layout

\begin_layout Description
变换
\begin_inset Formula $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}$
\end_inset

的余定义域 集合 
\begin_inset Formula $\mathbb{R}^{m}$
\end_inset

 包含变换 
\begin_inset Formula $T$
\end_inset

 的值域，通常，如果 
\begin_inset Formula $T$
\end_inset

 映射一个向量空间 
\begin_inset Formula $V$
\end_inset

 到另一个向量空间 
\begin_inset Formula $W$
\end_inset

, 那么 
\begin_inset Formula $W$
\end_inset

 被称为 
\begin_inset Formula $T$
\end_inset

 的余定义域.
 
\end_layout

\begin_layout Description
关于
\begin_inset Formula $T$
\end_inset

的
\begin_inset Formula $\mathcal{B}$
\end_inset

-矩阵 对 
\begin_inset Formula $V$
\end_inset

 中关于基 
\begin_inset Formula $\mathcal{B}$
\end_inset

 的一个线性变换: 
\begin_inset Formula $T:V\rightarrow V$
\end_inset

 对应的矩阵 
\begin_inset Formula $[T]_{\mathcal{B}}$
\end_inset

, 它具有如下的性质, 对 
\begin_inset Formula $V$
\end_inset

 中所有的 
\begin_inset Formula $\boldsymbol{x}$
\end_inset

, 
\begin_inset Formula $[T(\boldsymbol{x})]_{\mathcal{B}}=[\boldsymbol{T}]_{\mathcal{B}}[\boldsymbol{x}]_{\mathcal{B}}$
\end_inset

 成立.
\end_layout

\begin_layout Description
带形矩阵 一个矩阵, 它的非零元素位于主对角线的上下两侧的带形以内.
 
\end_layout

\begin_layout Description
最佳逼近 给定子空间中离给定向量的最近点.
 
\end_layout

\begin_layout Description
两对角线矩阵 一个非零元素位于主对角线和与主对角线相邻的一斜对角线上的矩阵.
 
\end_layout

\begin_layout Description
仿射变换 一个形如 
\begin_inset Formula $T(x)=Ax+b$
\end_inset

 的映射 
\begin_inset Formula $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}$
\end_inset

, 此处 
\begin_inset Formula $A$
\end_inset

 是 
\begin_inset Formula $m\times n$
\end_inset

 矩阵且 
\begin_inset Formula $b$
\end_inset

 属于 
\begin_inset Formula $\mathbb{R}^{m}$
\end_inset

.
 
\end_layout

\begin_layout Description
动力系统的吸引子 所有轨迹都趋于的点.
 
\end_layout

\begin_layout Description
辅助方程 一个关于变量 
\begin_inset Formula $r$
\end_inset

 的多项式方程, 来源于齐次差分方程的系数.
\end_layout

\end_body
\end_document