希尔伯特矩阵
希尔伯特矩阵 是一个正方形矩阵，它的每个元素都是一个单位分数。 属性:
- 它是一个对称矩阵。
-
Its determinant value is always positive.
示例:
``` Input : N = 2 Output : 1 0.5 0.5 0.33
Input : N = 3 Output : 1.0000 0.5000 0.3333 0.5000 0.3333 0.2500 0.3333 0.2500 0.2000
```
数学上，希尔伯特矩阵可以由给定的公式形成:
```
Let H be a Hilbert Matrix of NxN. Then H(i, j) = 1/(i+j-1)
```
下面是上述公式的基本实现。
C++
``` // C++ program for Hilbert Matrix
include
using namespace std;
// Function that generates a Hilbert matrix void printMatrix(int n) { float H[n][n];
for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) {
// using the formula to generate // hilbert matrix H[i][j] = (float)1.0 / ((i + 1) + (j + 1) - 1.0); } }
for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) cout << H[i][j] << " "; cout << endl; } }
// driver function int main() { int n = 3; printMatrix(n); return 0; } ```
Java 语言(一种计算机语言，尤用于创建网站)
``` // Java program for // Hilbert Matrix import java.io.*;
class GFG {
// Function that generates // a Hilbert matrix static void printMatrix(int n) { float H[][] = new float[n][n];
for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) {
// using the formula // to generate // hilbert matrix H[i][j] = (float)1.0 / ((i + 1) + (j + 1) - (float)1.0); } }
for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) System.out.print(H[i][j] + " "); System.out.println(); } }
// Driver code public static void main (String[] args) { int n = 3; printMatrix(n); } }
// This code is contributed // by anuj_67. ```
C
``` // C# program for Hilbert Matrix using System;
class GFG {
// Function that generates // a Hilbert matrix static void printMatrix(int n) { float[,] H = new float[n, n];
for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) {
// using the formula to generate // hilbert matrix H[i, j] = (float)1.0 / ((i + 1) + (j + 1) - (float)1.0); } }
for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) Console.Write(H[i, j] + " "); Console.WriteLine(""); } }
// Driver code public static void Main() { int n = 3; printMatrix(n); } }
// This code is contributed // by mits ```
Output:
``` 1 0.5 0.333333 0.5 0.333333 0.25 0.333333 0.25 0.2
```
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