# 查找矩阵的法线和迹线的程序 > 原文： [https://www.geeksforgeeks.org/program-find-normal-trace-matrix/](https://www.geeksforgeeks.org/program-find-normal-trace-matrix/) 给定 2D 矩阵，任务是找到矩阵的“迹线”和“法线”。 **矩阵的标准**定义为矩阵元素平方和的平方根。 n×n 方阵的 [**迹线**](https://en.wikipedia.org/wiki/Trace_(linear_algebra)) 是对角元素的总和。 **示例**： ``` Input : mat[][] = {{7, 8, 9}, {6, 1, 2}, {5, 4, 3}}; Output : Normal = 16 Trace = 11 Explanation : Normal = sqrt(7*7+ 8*8 + 9*9 + 6*6 + 1*1 + 2*2 + 5*5 + 4*4 + 3*3) = 16 Trace = 7+1+3 = 11 Input :mat[][] = {{1, 2, 3}, {6, 4, 5}, {2, 1, 3}}; Output : Normal = 10 Trace = 8 Explanation : Normal = sqrt(1*1 +2*2 + 3*3 + 6*6 + 4*4 + 5*5 + 2*2 + 1*1 + 3*3) Trace = 8(1+4+3) ```  ## C++ ```cpp // C++ program to find trace and normal // of given matrix #include<bits/stdc++.h> using namespace std; // Size of given matrix const int MAX = 100; // Returns Normal of a matrix of size n x n int findNormal(int mat[][MAX], int n) {     int sum = 0;     for (int i=0; i<n; i++)         for (int j=0; j<n; j++)             sum += mat[i][j]*mat[i][j];     return sqrt(sum); } // Returns trace of a matrix of size n x n int findTrace(int mat[][MAX], int n) {     int sum = 0;     for (int i=0; i<n; i++)          sum += mat[i][i];     return sum; } // Driven source int main() {     int mat[][MAX] = {{1, 1, 1, 1, 1},         {2, 2, 2, 2, 2},         {3, 3, 3, 3, 3},         {4, 4, 4, 4, 4},         {5, 5, 5, 5, 5},     };     cout << "Trace of Matrix = "          << findTrace(mat, 5) << endl;     cout << "Normal of Matrix = "          << findNormal(mat, 5) << endl;     return 0; } ``` ## Java ```java // Java program to find trace and normal // of given matrix import java.io.*; class GFG { // Size of given matrix static  int MAX = 100; // Returns Normal of a matrix of size n x n  static int findNormal(int mat[][], int n) {     int sum = 0;     for (int i=0; i<n; i++)         for (int j=0; j<n; j++)             sum += mat[i][j]*mat[i][j];     return (int)Math.sqrt(sum); } // Returns trace of a matrix of size n x n  static int findTrace(int mat[][], int n) {     int sum = 0;     for (int i=0; i<n; i++)         sum += mat[i][i];     return sum; } // Driven source public static void main (String[] args) {             int mat[][] = {{1, 1, 1, 1, 1},         {2, 2, 2, 2, 2},         {3, 3, 3, 3, 3},         {4, 4, 4, 4, 4},         {5, 5, 5, 5, 5},     };     System.out.println ("Trace of Matrix = "          + findTrace(mat, 5));     System.out.println ("Normal of Matrix = "          + findNormal(mat, 5));     } }  // This code is contributed by vt_m. ``` ## Python3 ```py # Python3 program to find trace and  # normal of given matrix  import math # Size of given matrix  MAX = 100;  # Returns Normal of a matrix  # of size n x n  def findNormal(mat, n):      sum = 0;      for i in range(n):          for j in range(n):              sum += mat[i][j] * mat[i][j];      return math.floor(math.sqrt(sum));  # Returns trace of a matrix of  # size n x n  def findTrace(mat, n):      sum = 0;      for i in range(n):          sum += mat[i][i];      return sum;  # Driver Code  mat = [[1, 1, 1, 1, 1],         [2, 2, 2, 2, 2],         [3, 3, 3, 3, 3],         [4, 4, 4, 4, 4],         [5, 5, 5, 5, 5]];  print("Trace of Matrix =", findTrace(mat, 5));  print("Normal of Matrix =", findNormal(mat, 5));  # This code is contributed by mits ``` ## C# ```cs // C# program to find trace and normal // of given matrix using System; class GFG {     // Returns Normal of a matrix of     // size n x n     static int findNormal(int [,]mat, int n)     {         int sum = 0;         for (int i = 0; i < n; i++)             for (int j = 0; j < n; j++)                 sum += mat[i,j] * mat[i,j];         return (int)Math.Sqrt(sum);     }     // Returns trace of a matrix of size      // n x n     static int findTrace(int [,]mat, int n)     {         int sum = 0;         for (int i = 0; i < n; i++)             sum += mat[i,i];         return sum;     }     // Driven source     public static void Main ()      {         int [,]mat = { {1, 1, 1, 1, 1},                        {2, 2, 2, 2, 2},                        {3, 3, 3, 3, 3},                        {4, 4, 4, 4, 4},                        {5, 5, 5, 5, 5},     };     Console.Write ("Trace of Matrix = "             + findTrace(mat, 5) + "\n");     Console.Write("Normal of Matrix = "                     + findNormal(mat, 5));     } }  // This code is contributed by nitin mittal. ``` ## PHP ```php <?php // PHP program to find trace and  // normal of given matrix // Size of given matrix $MAX = 100; // Returns Normal of a  // matrix of size n x n function findNormal($mat, $n) {     $sum = 0;     for ( $i = 0; $i < $n; $i++)         for ( $j = 0; $j < $n; $j++)             $sum += $mat[$i][$j] *                      $mat[$i][$j];     return floor(sqrt($sum)); } // Returns trace of a // matrix of size n x n function findTrace( $mat, $n) {     $sum = 0;     for ( $i = 0; $i < $n; $i++)         $sum += $mat[$i][$i];     return $sum; } // Driver Code $mat = array(array(1, 1, 1, 1, 1),              array(2, 2, 2, 2, 2),              array(3, 3, 3, 3, 3),              array(4, 4, 4, 4, 4),              array(5, 5, 5, 5, 5)); echo "Trace of Matrix = ",    findTrace($mat, 5),"\n"; echo "Normal of Matrix = " ,         findNormal($mat, 5) ; // This code is contributed by anuj_67\. ?> ``` **输出**： ``` Trace of matrix = 15 Normal of matrix = 16 ``` **时间复杂度**： O（n * n） **空间复杂度**：`O(1)` **参考**： [https://en.wikipedia.org/wiki/Trace_(linear_algebra）](https://en.wikipedia.org/wiki/Trace_(linear_algebra))