关于矩阵的一些操作（求转置矩阵、行列式、矩阵的秩、矩阵的逆矩阵、两个矩阵的乘积矩阵）

该程序的功能主要解决一些简单矩阵计算问题。

主要功能有：

① 矩阵输入

② 矩阵输出

③ 输出矩阵的转置矩阵（可转置任意行列的矩阵）

④ 求方阵的行列式（如果你输入错误，程序将提示你错误，你可关闭程序，重新输入行列相同的矩阵，再进行计算）

⑤ 求矩阵的秩

⑥ 求矩阵的逆矩阵（前提：行和列相等）

⑦ 求两个矩阵的乘积矩阵（其中之一是你已经输入的那一个矩阵，另一个你可自行输入，可计算多次乘积）

 /*
 author:wangchangshuai0010 sdust wangchangshuai0010.iteye.com
 */
 #include
 #include
 #define N 10

 void output(double a[][N],int am,int an)
 {
     int i,j;
     printf("\nThe OriginalMatrix A is:\n");
     printf("**********************************************\n");
     for(i=0;i
     {
        for(j=0;j
        {
            printf("%10.4f",a[i][j]);
        }
        printf("\n");
     }
 }



 void inver(double b[][N],int am,int an)
 {
     int i,j;
     double a[N][N],c[N][N];
     for(i=0;i
     {
         for(j=0;j
         {
             a[i][j]=b[i][j];
         }
     }
     for(i=0;i
     {
         for(j=0;j
         {
             c[j][i]=a[i][j];
         }
     }
     for(i=0;i
     {
        for(j=0;j
        {
            printf("%10.4f",c[i][j]);
        }
        printf("\n");
     }
 }

 double getdet(double b[][N],int am,int an)
 {
     int i,j,k,l,nexti,count=0;
     double temp,a[N][N],detA=1.0,x;
     for(i=0;i
     {
         for(j=0;j
         {
             a[i][j]=b[i][j];
         }
     }
     if(am==an)
     {
         for(i=0,j=0;i
         {
             nexti=i;
             while(a[i][j]==0)
             {
                 nexti++;
                 temp=a[i][j];
                 a[i][j]=a[nexti][j];
                 a[nexti][j]=temp;
             }
             for(k=j+1;k
             {
                 temp=a[i][k];
                 a[i][k]=a[nexti][k];
                 a[nexti][k]=temp;
             }
             for(l=i+1;l
             {
                 if(a[l][j]==0)
                 {l++;}
                 else
                 {
                     x=a[l][j]/a[i][j];
                     for(k=j;k
                     {

                         a[l][k]=a[l][k]-(x)*a[i][k];
                     }
                 }
             }
         }
         for(i=0,j=0;i
         {
             detA*=a[i][j];
         }
     }
     else
     {
         printf("error!\n");
     }
     return detA;
 }


 void getrank(double b[][N],int am,int an)
 {
     int i,s,j,k,l,nexti,t=0,count=0;
     double temp,x,a[N][N],detA=1.0;
     if(am>an)
     {
         s=am;
         am=an;
         an=s;
     }
     for(i=0;i
     {
         for(j=0;j
         {
             a[i][j]=b[i][j];
         }
     }
     for(i=0,j=0;i
     {
         nexti=i;
         while(a[i][j]==0)
         {
             nexti=i+1;
             temp=a[i][j];
             a[i][j]=a[nexti][j];
             a[nexti][j]=temp;
         }
         for(k=j+1;k
         {
             temp=a[i][k];
             a[i][k]=a[nexti][k];
             a[nexti][k]=temp;
         }
         for(l=i+1;l
         {
             if(a[l][j]==0)
             {l++;}
             else
             {
                 x=a[l][j]/a[i][j];
                 for(k=j;k
                 {
                     a[l][k]=a[l][k]-(x)*a[i][k];
                 }
             }
         }
     }
     for(i=an-1;i
     {
         for(j=am;j
         {
             if(a[i][j]!=0)
             {
                 t++;
             }
         }
     }
     if(t==0)
     {
         for(i=0,j=0;a[i][j]!=0&&i
         {count++;}
         printf("the rank is %d\n",count);
     }
     else
     {
         printf("**********************************************\n");
         printf("the rank is %d\n",am);
     }
 }



 void getnijuzhen(double b[][N],int am,int an)
 {
     int i,j,k,l,m,n;
     double a[N][N],c[N][N],d[N][N],x;
     if(an!=am)
     {
         printf("error!\n");
     }
     else{
       for(i=0;i
       {
         for(j=0;j
         {
             a[i][j]=b[i][j];
         }
       }
      for(i=0;i
      {
         for(j=0;j
         {
             m=i;
             n=j;
             for(k=0,m=0;k
             {
                 if(k==m)
                 {m++;}
                 for(l=0,n=0;l
                 {
                     if(l==j)
                     {n++;}
                     c[k][l]=a[m][n];
                 }
             }
             d[i][j]=getdet(c,an-1,an-1)*pow(-1,i+j);
         }
      }
      x=getdet(a,an,am);
      if(x==0)
      {
          printf("error!can't get nijuzhen!\n");
      }
      else
      {
      for(i=0;i
      {
         for(j=0;j
         {
             d[i][j]=d[i][j]/x;
         }
       }
      printf("the nijuzhen of the matrix is:\n");
      printf("**********************************************\n");
      inver(d,an,an);
      }
     }
 }


 void multiply(double c[N][N],int am,int an)
 {
     int i,j,k,bm,bn;
     double a[N][N],b[N][N],d[N][N];
     printf("please input the row and line of matrix B:\n");
     scanf("%d %d",&bm,&bn);
     if(an!=bm)
     {
         printf("error!\n");
     }
     else
     {
         printf("please input the matrix A:\n");
         for(i=0;i
         {
             for(j=0;j
             {
                 scanf("%lf",&b[i][j]);
             }
         }
         for(i=0;i
         {
             for(j=0;j
             {
                 a[i][j]=c[i][j];
             }
         }
         for(i=0;i
         {
             for(j=0;j
             {
                 d[i][j]=0;
                 for(k=0;k
                     d[i][j]+=a[i][k]*b[k][j];
             }
         }
         printf("the multiply of A and B is：\n");
         printf("**********************************************\n");
         for(i=0;i
         {
             for(j=0;j
             {
                 printf("%10.4lf",d[i][j]);
             }
             printf("\n");
         }
     }
 }




 void main()
 {
    int m,n,i,j,select;
    double a[N][N],detA;
    printf("please input the row and line of matrix A:\n");
    scanf("%d %d",&m,&n);
    printf("please input the matrix A:\n");
    for(i=0;i
    {
      for(j=0;j
      {
          scanf("%lf",&a[i][j]);
      }
    }
    do
    {
        printf("**********************************************\n");
        printf("1-->output\n2-->inver\n3-->get detmination\n4->get rank\n5-->get nijuzhen\n6->get multiply of two matrixs\n0-->exit!\n");
        printf("**********************************************\n");
        do
        {
            printf("Please input your choice:\n(Warming:Please input number from 0 to 6,or it will be error!)\n");
            scanf("%d",&select);
            if(select>6||select<0)
            {
                printf("Error!please input the number again!\n");
            }
        }while(select>6||select<0);
              switch(select)
              {
              case 1:
                  output(a,m,n);
                  break;
              case 2:
                  printf("\nThe InverseMatrix is:\n");
                  printf("**********************************************\n");
                  inver(a,m,n);
                  break;
              case 3:
                  detA=getdet(a,m,n);
                  printf("the detmination is %.4lf\n",detA);
                  break;
              case 4:
                  getrank(a,m,n);
                  break;
              case 5:
                  getnijuzhen(a,m,n);
                  break;
              case 6:
                  multiply(a,m,n);
              default:
                  break;
              }
          }while(select!=0);
 }