對角線

Multi tool use
Multi tool use






立方體對角線




線分對角線


在數學上，對角線有多個定義:



多邊形


在多邊形上，對角線是連結兩個不毗鄰頂點的線段。若且唯若多邊形的對角線在多邊形之內，該多邊形是凸多边形。


對角線數目的求法：當n是多邊形的頂點的數目，每個頂點除了它本身和毗鄰的兩邊之外，都有對角線連接到其他頂點。這樣乘以頂點的數目就是(n−3)∗n{displaystyle (n-3)*n}(n-3)*n。因為每個頂點計算了兩次，所以再除以2就得出對角線的數目為


d=n2−3n2.{displaystyle d={frac {n^{2}-3n}{2}}.,}d={frac {n^{2}-3n}{2}}.,


矩陣


在正方形矩陣中，有些對角線有特殊的稱呼。


[a11a12a13a21a22a23a31a32a33]{displaystyle {begin{bmatrix}a_{11}&a_{12}&a_{13}\a_{21}&a_{22}&a_{23}\a_{31}&a_{32}&a_{33}end{bmatrix}}}{begin{bmatrix}a_{{11}}&a_{{12}}&a_{{13}}\a_{{21}}&a_{{22}}&a_{{23}}\a_{{31}}&a_{{32}}&a_{{33}}end{bmatrix}}






















名稱
 定義
 在上面的矩陣，該對角線上的元素
主對角線
 由左上至右下的對角線
a11,a22,a33{displaystyle a_{11},a_{22},a_{33}}a_{{11}},a_{{22}},a_{{33}}
次對角線
 右上至左下的對角線
a13,a22,a31{displaystyle a_{13},a_{22},a_{31}}a_{{13}},a_{{22}},a_{{31}}
超對角線
 剛好在主對角線上面一格或右邊的元素。
a12,a23{displaystyle a_{12},a_{23}}a_{{12}},a_{{23}}



  • 單位矩陣可以說是有元素1在主對角線，而其他元素皆是0的矩陣。


  • 對角線矩陣是主對角線以外的元素均為0的矩陣。



幾何








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