线性代数公式汇总

行列式

AT=A;kA=knA;AB=AB;A=An1;A1=A1=1A;ABA=B.\begin{aligned} & \large |A^T|=|A|; \quad\quad\quad\quad |kA|=k^n|A|;\\ & \large |AB|=|A||B|; \quad\quad\quad\quad |A^*|=|A|^{n-1};\\ & \large |A^{-1}|=|A|^{-1}=\frac{1}{|A|}; \quad\quad\quad\quad A\sim B \longrightarrow |A|=|B|.\\ \end{aligned}

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高等数学公式汇总

等价无穷小

sinxtanxarcsinxarctanxln(1+x)ex1xxsinx16x3xarcsinx16x3xtanx13x3xarctanx13x31cosx12x21cosaxa2x2ax1xlna(1+x)a1ax\begin{aligned} & \large \sin{x} \sim \tan{x} \sim \arcsin{x} \sim \arctan{x} \sim \ln(1+x) \sim \text{e}^x-1 \sim x \\ & \large x-\sin{x} \sim \frac{1}{6}x^3 \quad\quad\quad\quad x-\arcsin{x} \sim -\frac{1}{6}x^3 \\ & \large x-\tan{x} \sim -\frac{1}{3}x^3 \quad\quad\quad\quad x-\arctan{x} \sim -\frac{1}{3}x^3 \\ & \large 1-\cos{x} \sim \frac{1}{2}x^2 \quad\quad\quad\quad 1-\cos^ax \sim \frac{a}{2}x^2 \\ & \large a^x-1 \sim x\ln a \quad\quad\quad\quad (1+x)^a-1 \sim ax \\ \end{aligned}

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