Basic Matrix knowledge

字数统计: 275阅读时长: 1 min

 2018/09/17  38  Share

⎡ ⎢ ⎣ \begin{matrix} a & b & c d & e & f \end{matrix} ⎤ ⎥ ⎦

$\begin{bmatrix}a&b&c\\\\d&e&f\end{bmatrix}$

${A}\times{B} \neq {B}\times{A}$

${E}\times{A}={A}\times{E}$

(E is a constant 如果E为常数)

The all multiplication rules are true when E is a constatnt matrix except commutative rule.（当E为常数时，所有的乘法准则都将成立，交换路除外）

${A{ij}=(-1)^{i+j}{M{ij}}}$

${M{ij}}$

if（如果有）：

$D=\begin{vmatrix}a{11}&a{12}&a{13}\\\\a{21}&a{22}&a{23}\\\\a{31}&a{32}&a{33}\end{vmatrix}$

that（那么）:

the complement of a11 is （a11的余子式）:

${M{11}=}\begin{vmatrix}a{22}&a{23}\\\\a{32}&a{33}\end{vmatrix}$

the Algebraic complement of a11 is （a11的代数余子式）:

${A{11}=(-1)^{1+1}{M{11}}}$

${A^{-1}= \frac{1}{\begin{vmatrix}A\end{vmatrix}}{A^{*}}}$

${A^{*}}$

${AB}=E,\;{BA=E} \Rightarrow B=A^{-1}\;(E\;is\;unit\;matrix\;E为单位阵)$

$\begin{bmatrix}a&b\\\\c&d\\\\e&f\end{bmatrix}^{T}\;=\quad\begin{bmatrix}a&c&e\\\\b&d&f\end{bmatrix}$

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