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.
Here is the source code of the Java Program to Find Basis and Dimension of a Matrix. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.
//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(); } }
Output:
$ javac Basis_Dimension_Matrix.java $ java Basis_Dimension_Matrix 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
Related posts:
Jackson – Unmarshall to Collection/Array
Spring Security Login Page with React
Adding Shutdown Hooks for JVM Applications
REST Web service: Upload và Download file với Jersey 2.x
Overview of Spring Boot Dev Tools
Flattening Nested Collections in Java
Getting the Size of an Iterable in Java
ETL with Spring Cloud Data Flow
A Guide to Java SynchronousQueue
Spring Boot Annotations
Java Program to Implement LinkedBlockingQueue API
Call Methods at Runtime Using Java Reflection
Hướng dẫn Java Design Pattern – MVC
Java Program to Implement Sorted Circularly Singly Linked List
Practical Java Examples of the Big O Notation
Most commonly used String methods in Java
Java Program to Generate N Number of Passwords of Length M Each
Disable Spring Data Auto Configuration
Spring REST with a Zuul Proxy
Java Program to Implement Doubly Linked List
The Guide to RestTemplate
Spring Boot - Admin Server
Giới thiệu Aspect Oriented Programming (AOP)
Java Program to Generate Random Partition out of a Given Set of Numbers or Characters
Guava Collections Cookbook
How to Round a Number to N Decimal Places in Java
Automatic Property Expansion with Spring Boot
Java Program to Find k Numbers Closest to Median of S, Where S is a Set of n Numbers
Java – Byte Array to Reader
Java Program to Construct an Expression Tree for an Infix Expression
Spring’s RequestBody and ResponseBody Annotations
Introduction to Liquibase Rollback