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