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更新行列式

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Didnelpsun
2021-07-02 23:24:24 +08:00
parent 6cb46ac98b
commit fb1bcfc4b1
4 changed files with 40 additions and 8 deletions
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linear-algebra/knowledge/1-determinant/determinant.pdf
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linear-algebra/knowledge/1-determinant/determinant.tex
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@@ -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$\sum\limits_{1\leqslant j<i\leqslant n}(a_i-a_j)$。
范德蒙德行列式：元素连乘，结果为$\prod\limits_{1\leqslant j<i\leqslant n}(a_i-a_j)$。
若一个四阶范德蒙德行列式的结果为$(a_4-a_1)(a_4-a_2)(a_4-a_3)(a_3-a_1)(a_3-a_2)(a_2-a_1)$。
\end{multicols}