我想找到在C＃4x4矩阵的行列式 [英] i want to find determinant of 4x4 matrix in c#

问题描述

可能重复：结果
的计算n×n的矩阵行列式C＃

我想找到的决定因素在C＃4x4矩阵的，请帮助紧急

  INT SS = 4;诠释计数= 0; 
 INT [，]矩阵=新的INT [SS，SS] 
 ArrayList的人=新的ArrayList（）{} 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16; 
的for（int i = 0; I< SS，我++）
 {
为（INT J = 0; J< SS; J ++）
 {
矩阵[I，J] = Convert.ToInt32（人[计数]）; 
 ++计数; 
的Response.Write（矩阵[I，J] +）; 
} 
的Response.Write（< BR />中）; 
} 
  

解决方案

如果你是固定4×4，最简单的办法是只硬编码的公式。

  //假设矩阵指数从0（0,1开始，图2和3）
公共双行列式（INT [，]米）{
返回
M [0,3] * M [1,2] * M [2,1] *米[ 3,0]  - 米[0,2] * M [1,3] * M [2,1] *米[3,0]  -  
M [0,3] * M [1,1] *米[2,2] * M [3,0] + M [0,1] * M [1,3] * M [2,2] * M [3,0] + 
M [0,2 ] * M [1,1] * M [2,3] * M [3,0]  - 米[0,1] * M [1,2] * M [2,3] * M [3,0] -  
M [0,3] * M [1,2] * M [2,0] * M [3,1] + M [0,2] * M [1,3] * M [2,1 0] * M [3,1] + 
M [0,3] * M [1,0] * M [2,2] *米[3,1]  - 米[0,0] *米[ 1,3] * M [2,2] *米[3,1]  -  
M [0,2] * M [1,0] * M [2,3] * M [3,1] +米[0,0] * M [1,2] * M [2,3] * M [3,1] + 
M [0,3] * M [1,1] * M [2,0 ] * M [3,2]  - 米[0,1] * M [1,3] * M [2,0] * M [3,2]  -  
M [0,3] *米[1 ，0] * M [2,1] * M [3,2] + M [0,0] * M [1,3] * M [2,1] * M [3,2] + 
M [0,1] * M [1,0] * M [2,3] * M [3,2]  - 米[0,0] * M [1,1] * M [2,3] *米[ 3,2]  -  
M [0,2] * M [1,1] * M [2,0] * M [3,3] + M [0,1] * M [1,2] *米[2,0] * M [3,3] + 
M [0,2] * M [1,0] * M [2,1] * M [3,3]  - 米[0,0 ] * M [1,2] * M [2,1] * M [3,3]  -  
M [0,1] * M [1,0] * M [2,2] * M [3 1,3] + M [0,0] * M [1,1] * M [2,2] * M [3,3]; 
} 
  

参考

• 维基/行列式


• EuclidianSpace.com/Determinant 4x4的公式

Possible Duplicate:
calculate nxn matrix determinant C#

i want to find determinant of 4x4 matrix in c# please help urgent

    int ss = 4; int count = 0;
    int[,] matrix=new int[ss,ss];
    ArrayList al = new ArrayList() {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 };
    for (int i = 0; i < ss; i++)
    {
        for (int j = 0; j < ss; j++)
        {
            matrix[i, j] =Convert.ToInt32( al[count]);
            ++count;
            Response.Write(matrix[i, j] + " ");
        }
        Response.Write("<br/>");
    }

解决方案

If you're fixed to 4x4, the simplest solution would be to just hardcode the formula.

   // assumes matrix indices start from 0 (0,1,2 and 3)
   public double determinant(int[,] m) {
      return
         m[0,3] * m[1,2] * m[2,1] * m[3,0] - m[0,2] * m[1,3] * m[2,1] * m[3,0] -
         m[0,3] * m[1,1] * m[2,2] * m[3,0] + m[0,1] * m[1,3] * m[2,2] * m[3,0] +
         m[0,2] * m[1,1] * m[2,3] * m[3,0] - m[0,1] * m[1,2] * m[2,3] * m[3,0] -
         m[0,3] * m[1,2] * m[2,0] * m[3,1] + m[0,2] * m[1,3] * m[2,0] * m[3,1] +
         m[0,3] * m[1,0] * m[2,2] * m[3,1] - m[0,0] * m[1,3] * m[2,2] * m[3,1] -
         m[0,2] * m[1,0] * m[2,3] * m[3,1] + m[0,0] * m[1,2] * m[2,3] * m[3,1] +
         m[0,3] * m[1,1] * m[2,0] * m[3,2] - m[0,1] * m[1,3] * m[2,0] * m[3,2] -
         m[0,3] * m[1,0] * m[2,1] * m[3,2] + m[0,0] * m[1,3] * m[2,1] * m[3,2] +
         m[0,1] * m[1,0] * m[2,3] * m[3,2] - m[0,0] * m[1,1] * m[2,3] * m[3,2] -
         m[0,2] * m[1,1] * m[2,0] * m[3,3] + m[0,1] * m[1,2] * m[2,0] * m[3,3] +
         m[0,2] * m[1,0] * m[2,1] * m[3,3] - m[0,0] * m[1,2] * m[2,1] * m[3,3] -
         m[0,1] * m[1,0] * m[2,2] * m[3,3] + m[0,0] * m[1,1] * m[2,2] * m[3,3];
   }

References

• Wikipedia/Determinant
• EuclidianSpace.com/Determinant 4x4 formula

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