矩阵运算

矩阵快速幂

矩阵快速幂

矩阵加法

只有同型矩阵才能进行加减法（即行数与列数都相同）

#include
#include
#include
#include
#include
#include
using namespace std;
#define MAX 105
int main(int argc, char const *argv[])
{
  int A[MAX][MAX];
  int B[MAX][MAX];
  int ans[MAX][MAX];
  memset(A, 0, sizeof(A));
  memset(B, 0, sizeof(B));
  memset(ans, 0, sizeof(ans));
  int line, row;
  cin >> line >> row;
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      cin >> A[i][j];
    }
  }
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      cin >> B[i][j];
    }
  }
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      ans[i][j] = A[i][j] + B[i][j];
    }
  }
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      cout << ans[i][j] << " ";
    }
    cout << endl;
  }



}

矩阵减法

#include
#include
#include
#include
#include
#include
using namespace std;
#define MAX 105
int main(int argc, char const *argv[])
{
  int A[MAX][MAX];
  int B[MAX][MAX];
  int ans[MAX][MAX];
  memset(A, 0, sizeof(A));
  memset(B, 0, sizeof(B));
  memset(ans, 0, sizeof(ans));
  int line, row;
  cin >> line >> row;
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      cin >> A[i][j];
    }
  }
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      cin >> B[i][j];
    }
  }
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      ans[i][j] = A[i][j] - B[i][j];
    }
  }
  for(int i = 1; i <= line; ++i){
    for(int j = 1; j <= row; ++j){
      cout << ans[i][j] << " ";
    }
    cout << endl;
  }



}

矩阵乘法

两个矩阵可以相乘的条件：第一个矩阵的列数必须等于第二个矩阵的行数

第一个矩阵：n * m      第二个矩阵：m * r（可以运算）

第一个矩阵：n * m      第二个矩阵：s * r（不可以运算）

#include
#include
#include
#include
#include
#include
using namespace std;
#define MAX 105
int main(int argc, char const *argv[])
{
  int A[MAX][MAX];
  int B[MAX][MAX];
  int ans[MAX][MAX];
  memset(A, 0, sizeof(A));
  memset(B, 0, sizeof(B));
  memset(ans, 0, sizeof(ans));    //初始化各矩阵
  int a_line, a_row, b_line, b_row;
  cin >> a_line >> a_row;
  for(int i = 1; i <= a_line; ++i){
    for(int j = 1; j <= a_row; ++j){
      cin >> A[i][j];
    }
  }
  cin >> b_line >> b_row;
  for(int i = 1; i <= b_line; ++i){
    for(int j = 1; j <= b_row; ++j){
      cin >> B[i][j];
    }
  }
  if(a_row != b_line){    //第一个列数不等于第二个行数，不能进行运算
   printf("Error: %d != %d\n", a_row, b_line);
  }
  else{
    for(int i = 1; i <= a_line; ++i){
      for(int j = 1; j <= b_row; ++j){
        for(int k = 1; k <= a_row; ++k){
          ans[i][j] += A[i][k] * B[k][j];
        }
      }
    }
  cout << a_line << " " << b_row << endl;
  for(int i = 1; i <= a_line; ++i){
    for(int j = 1; j <= b_row; ++j){
      if(j != b_row)
      cout << ans[i][j] << " ";
      else
        cout << ans[i][j];
      }
      cout << endl;
    }
  }
}