From fb1bcfc4b1d0c31c0cd64ba213d5e01ab2f82fa6 Mon Sep 17 00:00:00 2001 From: Didnelpsun <2675350965@qq.com> Date: Fri, 2 Jul 2021 23:24:24 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E8=A1=8C=E5=88=97=E5=BC=8F?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../exercise/1-determinant/determinant.pdf | Bin 141169 -> 98184 bytes .../exercise/1-determinant/determinant.tex | 40 ++++++++++++++++-- .../knowledge/1-determinant/determinant.pdf | Bin 83719 -> 84450 bytes .../knowledge/1-determinant/determinant.tex | 8 ++-- 4 files changed, 40 insertions(+), 8 deletions(-) diff --git a/linear-algebra/exercise/1-determinant/determinant.pdf b/linear-algebra/exercise/1-determinant/determinant.pdf index b70ff7af0bdfe5863550bdb6d99712ceb86e5e3b..11f64dfba0557602d7100d1c02634b0d0d747f1b 100644 GIT binary patch delta 94627 zcmZ6yLtrjU)Fd1yH@2-C+qP}nwv#8eZQHhu8{4++WZwUuS01WXBQ_^LtAK%jq8l5+C>J$&{rN&y?isf)-hx*7*YYFFc-IQ(b{T_ 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b/linear-algebra/exercise/1-determinant/determinant.tex @@ -86,7 +86,7 @@ $\therefore\,-a_{11}a_{23}a_{32}a_{44}+a_{11}a_{23}a_{34}a_{42}$。 \subsection{基本行列式与计算} -\subsubsection{三角行列式} +\subsubsection{主对角线行列式} $\left|\begin{array}{cccc} a_{11} & a_{12} & \cdots & a_{1n} \\ @@ -107,7 +107,7 @@ $\left|\begin{array}{cccc} & & & a_{nn} \end{array}\right|=a_{11}\cdots a_{nn}$ -\subsubsection{反三角行列式} +\subsubsection{副对角线行列式} $\left|\begin{array}{cccc} & & & a_{1n} \\ @@ -135,10 +135,12 @@ $\left|\begin{array}{cccc} a_1 & a_2 & \cdots & a_n \\ \cdots & \cdots & \vdots & \cdots \\ a_1^{n-1} & a_2^{n-1} & \cdots & a_n^{n-1} \\ -\end{array}\right|=\sum\limits_{1\leqslant j}j|c*E@Eys2oGQp8vwvq7=1 zUbpvdg&&7=fnRgvF4Puv>&v~@BSrd(U(a4IKM!x_rvd;`$vxBJJ&&3}I)SJ*c@xF$ znv+vdLKS!#XwW~KhMl)3g9yV-Vi$fKSEc|KOyoK_NlYLfAgJ}VjWwY9^+F(Fpu+Wr z^Bcmlj}Bi56g&z=tm3R>p>Cvhc$)W5K3aA%tY)8kn$!fmjbLIt;sPHu*Vc8v`eQy* zn599);ihrRVE8YcWfECaDv;I`lVa%okV4Eo+WW9tznh79(KNmThikWoX4zS!!*&27 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za%Ev{3V7Nz)45UQX9N{dKtx4Ac85(6R6t}LL3U6PS%!5O7c?{R0gNm| zGa@1~5}(1qDkI;*#0bu=tx4ZgE((!SYRG?uT!d{%gDV)bye1Qx23SXkk zVm~Bi!z_&8DLjp5FdNTee-7qi9_E`=rJ1)V#`~tq2`^E6V5(94Lazd4lAh?mEvcp{XsgqKm%_<_%H)70OvI#=%HiD^C+ z%HmHi3DZ(xD9f4h)U=uxN^;oCm}z}4l+Dae#!Xv)LfP5%^30U_?(?)M{V}Yje|woT z%kJ@c!mRk0&(F=GD^1}nM89}hG;8_n^W@1HN&5U6S8xs2aTB*Og=u_?@9~4#;8*EC Xw;n-;m%2#-9ttoyG72RnMNdWwcKwD^ diff --git a/linear-algebra/knowledge/1-determinant/determinant.tex b/linear-algebra/knowledge/1-determinant/determinant.tex index 7bdc41e..c9cb538 100644 --- a/linear-algebra/knowledge/1-determinant/determinant.tex +++ b/linear-algebra/knowledge/1-determinant/determinant.tex @@ -132,7 +132,7 @@ $\alpha_1=[a_{11},a_{12},\cdots,a_{1n}]$,$\alpha_2=[a_{21},a_{22},\cdots,a_{2n \subsection{特殊行列式} -\subsubsection{三角行列式} +\subsubsection{主对角线行列式} $\left|\begin{array}{cccc} a_{11} & a_{12} & \cdots & a_{1n} \\ @@ -155,13 +155,11 @@ $\left|\begin{array}{cccc} 上三角行列式:包括主对角线的右上部分元素不全为0,左下部分元素全为0。 - 下三角行列式:包括主对角线的左下部分元素不全为0,右上部分元素全为0。 - 对角行列式:省略号处的元素不全为0,其他主对角线外的元素全为0。 -\subsubsection{反三角行列式} +\subsubsection{副对角线行列式} $\left|\begin{array}{cccc} & & & a_{1n} \\ @@ -195,7 +193,7 @@ $\left|\begin{array}{cccc} a_1^{n-1} & a_2^{n-1} & \cdots & a_n^{n-1} \\ \end{array}\right|$ - 范德蒙德行列式:元素连乘,结果为$\sum\limits_{1\leqslant j