A Hilbert matrix is defined as:
where
and
Example:
In this post I have written a code that generates Hilbert matrices using C language.
CODE:
/*******************************
****HILBERT MATRIX GENERATOR****
*******************************/
#include<stdio.h>
/********
Function that generates a Hilbert matrix
Parameters:
no. of rows: m,
no. of coulmns: n,
a matrix of size mxn that would store the Hilbert matrix
********/
void Hilbert(int m, int n, double H[m][n]){
int i,j;
for(i=0;i<m;i++){
for(j=0;j<n;j++){
H[i][j]=(double)1.0/((i+1)+(j+1)-1.0);
}
}
}
/*******
Function that prints the elements of a matrix row-wise
Parameters: rows(m),columns(n),matrix[m][n]
*******/
void printMatrix(int m, int n, double matrix[m][n]){
int i,j;
for(i=0;i<m;i++){
for(j=0;j<n;j++){
printf("%lf\t",matrix[i][j]);
}
printf("\n");
}
}
int main(){
int m,n,i,j;
printf("Enter the size of the Hilbert matrix you want to generate:\nNo. of rows (m): ");
scanf("%d",&m);
printf("\nNo. of columns (n): ");
scanf("%d",&n);
double H[m][n];
Hilbert(m,n,H);
printf("\nThe reequired Hilbert matrix is:\n");
printMatrix(m,n,H);
}
OUTPUT:
Android Apps:
I’ve also created a few Android apps that perform various matrix operations and can come in handy to those taking a course on Numerical Methods.
Download: https://play.google.com/store/apps/details?id=com.bragitoff.numericalmethods
Download: https://play.google.com/store/apps/details?id=com.bragitoff.matrixcalculator
References and resources:
https://en.wikipedia.org/wiki/Hilbert_matrix
http://mathworld.wolfram.com/HilbertMatrix.html
http://reference.wolfram.com/language/ref/HilbertMatrix.html
Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.