在 GF(2) 的 MATLAB 中定义矩阵

Question

我以前从未使用过 MATLAB，但我必须执行一项操作来处理 25(row) x 25(col) 的矩阵。所以我不想手动做这个。所以我必须使用matlab。

我想在 GF(2) 的 MATLAB 中定义矩阵（2 阶的伽罗瓦域是一种称为域的数学结构，它提供了算术模二的正式定义）。

以下是我从命令 null(MATRIX,'r') 获取空空间的 5x5 矩阵

1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
1   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   1   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   1   1   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
1   0   0   0   0   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   1   0   0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   1   0   0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   1   0   0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   1   0   0   0   1   1   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   1   0   0   0   0   1   1   0   0   0   1   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   1   0   0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   1   0   0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   0   0   0   1   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   0   0   0   0   1   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   1   1   0   0   0   1   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   0   0   0   1   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   0   0   0   1   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   0   0   0   1   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   0   0   0   0   1   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   1   1   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1   1   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   1  

以下是我的 6x6 矩阵，当我尝试命令 null(MATRIX,'r') 时得到空结果

1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1

谁能告诉我是什么原因？

Answer 1

既然矩阵的所有元素都是这样写的，只需写A=[，然后复制矩阵，然后输入];。例如，如果你的矩阵是

1 2 3
4 5 6
7 8 9

那么你就可以了

A=[1 2 3
   4 5 6
   7 8 9];

然后查找使用的空空间null(A)。

Answer 2

对于第二部分，你可以只使用matlab中的“null”函数吗？ http://www.mathworks.com/help/matlab/ref/null.html

对于第一部分，也许这会有所帮助：Learning to build band matrices in MATLAB

您正在尝试制作对角线上也有 1 个向上 5 和向下 5 的带状矩阵。要制作那些，我认为您可以这样做

[m,n] = size(A);
i = 1;
for j = 6:n
    A(i,j) = 1;
    i = i+1;
end

这将产生上对角线。做低级，就做

j = 1;
for i = 6:n
    A(i,j) = 1;
    j = j+1;
end

Answer 3

构造这种带状矩阵的更简单方法是

A=toeplitz([1 1 0 0 0 0 1 zeros(1,18)])

我的经验法则：每次 for 循环都无法有效使用 Matlab。