You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
81 lines
2.7 KiB
Java
81 lines
2.7 KiB
Java
/*
|
|
|
|
This is the java program to find whether the vectors entered by users form the basis for the given dimension.
|
|
The result for the same can be obtained by checking whether the determinant of the matrix formed by vectors is zero or not.
|
|
If the determinant is non zero its forms the basis for the given dimension, not otherwise.
|
|
*/
|
|
|
|
//This is a sample program to find the basis and dimension of a vectors
|
|
import java.util.Scanner;
|
|
|
|
public class Basis_Dimension_Matrix
|
|
{
|
|
public static double determinant(double A[][],int N)
|
|
{
|
|
double det=0;
|
|
if(N == 1)
|
|
{
|
|
det = A[0][0];
|
|
}
|
|
else if (N == 2)
|
|
{
|
|
det = A[0][0]*A[1][1] - A[1][0]*A[0][1];
|
|
}
|
|
else
|
|
{
|
|
det=0;
|
|
for(int j1=0; j1<N; j1++)
|
|
{
|
|
double[][] m = new double[N-1][];
|
|
for(int k=0; k<(N-1); k++)
|
|
{
|
|
m[k] = new double[N-1];
|
|
}
|
|
for(int i=1; i<N; i++)
|
|
{
|
|
int j2=0;
|
|
for(int j=0; j<N; j++)
|
|
{
|
|
if(j == j1)
|
|
continue;
|
|
m[i-1][j2] = A[i][j];
|
|
j2++;
|
|
}
|
|
}
|
|
det += Math.pow(-1.0,1.0+j1+1.0)* A[0][j1] * determinant(m,N-1);
|
|
}
|
|
}
|
|
return det;
|
|
}
|
|
|
|
public static void main(String args[])
|
|
{
|
|
Scanner sc = new Scanner(System.in);
|
|
System.out.println("Enter the number of vectors:");
|
|
int n = sc.nextInt();
|
|
double [][]mat = new double[n][n];
|
|
System.out.println("Enter the vectors one by one:");
|
|
for(int i=0; i<n; i++)
|
|
{
|
|
for(int j=0; j<n; j++)
|
|
{
|
|
mat[j][i] = sc.nextDouble();
|
|
}
|
|
}
|
|
double det = determinant(mat, n);
|
|
if(det != 0)
|
|
System.out.println("The vectors froms the basis of R"+n+" as the determinant is non-zero");
|
|
else
|
|
System.out.println("The vectors doesn't form the basis of R"+n+" as the determinant is zero");
|
|
sc.close();
|
|
}
|
|
}
|
|
|
|
/*
|
|
Enter the number of vectors:
|
|
2
|
|
Enter the vectors one by one:
|
|
1 1
|
|
-1 2
|
|
The vectors froms the basis of R2 as the determinant is non-zero
|