线性代数常用的公式LaTeX表示
1.Am×nA_{m\times n}Am×n?的矩陣A=[a11a12?a1na21a22?a2n????am1am2?amn]A=\left[\begin{array}{cccc}{a_{11}} & {a_{12}} & {\cdots} & {a_{1 n}} \\ {a_{21}} & {a_{22}} & {\cdots} & {a_{2 n}} \\ {\vdots} & {\vdots} & {\ddots} & {\vdots} \\ {a_{m 1}} & {a_{m 2}} & {\cdots} & {a_{m n}}\end{array}\right] A=??????a11?a21??am1??a12?a22??am2???????a1n?a2n??amn????????
$$ A=\left[\begin{array}{cccc}{a_{11}} & {a_{12}} & {\cdots} & {a_{1 n}} \\ {a_{21}} & {a_{22}} & {\cdots} & {a_{2 n}} \\ {\vdots} & {\vdots} & {\ddots} & {\vdots} \\ {a_{m 1}} & {a_{m 2}} & {\cdots} & {a_{m n}}\end{array}\right] $$2.矩陣與向量相乘A?x?=(a11x1+a12x2+?+a1nxna21x1+a22x2+?+a2nxn?am1x1+am2x2+?+amnxn)A \cdot \vec{x}=\left(\begin{array}{c}{a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}} \\ {a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}} \\ {\vdots} \\ {a_{m 1} x_{1}+a_{m 2} x_{2}+\cdots+a_{m n} x_{n}}\end{array}\right) A?x=??????a11?x1?+a12?x2?+?+a1n?xn?a21?x1?+a22?x2?+?+a2n?xn??am1?x1?+am2?x2?+?+amn?xn????????
$$ A \cdot \vec{x}=\left(\begin{array}{c}{a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}} \\ {a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}} \\ {\vdots} \\ {a_{m 1} x_{1}+a_{m 2} x_{2}+\cdots+a_{m n} x_{n}}\end{array}\right) $$3.特征表示Ax=λxA x=\lambda x Ax=λx
$$ A x=\lambda x $$4.矩陣相似A=P?1BPA=P^{-1} B P A=P?1BP
$$ A=P^{-1} B P $$總結
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