寻找矩阵法线和轨迹的 Java 程序
原文:https://www . geesforgeks . org/Java-program-to-find-the-normal-and-trace-of-a-matrix/
对于给定的 2D 矩阵，目的是找到矩阵的迹和法向。
矩阵的法线定义为矩阵所有元素平方和的平方根。
给定方阵的迹定义为对角线上所有元素的和。
示例:
Input : matrix[][] = {{1, 4, 4},
{2, 3, 7},
{0, 5, 1}};
Output : Normal = 11
Trace = 5
Explanation :
Normal = sqrt(1*1+ 4*4 + 4*4 + 2*2 +
3*3 + 7*7 + 0*0 + 5*5 + 1*1)
= 11
Trace = 1+3+1 = 5
Input :matrix[][] = {{8, 9, 11},
{0, 1, 15},
{4, 10, -7}};
Output : Normal = 25
Trace = 2
Explanation :
Normal = sqrt(8*8 +9*9 + 11*11 + 0*0 + 1*1 +
15*15 + 4*4 + 10*10 + -7*-7) = 25
Trace = (8+1-7) = 2
示例:
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find the trace
// and normal of the given matrix
import java.io.*;
class geeksforgeeks {
// Dimension of the given matrix
static int max = 50;
// Finds Normal of the given
// matrix of size N x N
static int Normal(int matrix[][], int N)
{
// Initializing sum
int s = 0;
for (int j = 0; j < N; j++)
for (int k = 0; k < N; k++)
s += matrix[j][k] * matrix[j][k];
return (int)Math.sqrt(s);
}
// Finds trace of the given
// matrix of size N x N
static int Trace(int matrix[][], int N)
{
int s = 0;
for (int j = 0; j < N; j++)
s += matrix[j][j];
return s;
}
// The Driver code
public static void main(String[] args)
{
int matrix[][] = {
{ 2, 3, 5, 6, 7 }, { 8, 9, 10, 11, 12 },
{ 13, 14, 15, 16, 17 }, { 18, 1, 3, 0, 6 },
{ 7, 8, 11, 8, 11 },
};
System.out.println("Trace of the Matrix is: "
+ Trace(matrix, 5));
System.out.println("Normal of the Matrix is: "
+ Normal(matrix, 5));
}
}
Output
Trace of the Matrix is: 37
Normal of the Matrix is: 50
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