Matrix Determinant, Matrix Adjoint and Matrix Inverse
The Java program implements following three important matrix operation in this code. and these operation is applied on a square matrix size of 3x3. They are,
- Matrix Determinant
- Matrix singular or not
- Adjoint matrix
- Matrix Inversion
- AA-1 = I
- (A-1)-1 = A
Matrix Determinant - algorithm
matrix A - a matrix size of 3x3
A-cofactor(0,c) - read cofactor matrix of 0th row and cth column of the matrix A
set M[] =0
set D=0
Read matrix A
For c=0 : A-column
matrix cf = A-cofactor(0,c)
M[c]=cf[[0][0]*cf[[1][1] - cf[[0][1]*cf[[1][0]
End
For c=1 : A-column
D = D + pow(-1,c+0) *M[c]
End
print "determinant" D
Matrix Inverse - algorithm
matrix A - a matrix size of 3x3.
determinant(matrix A) - function finds and returns determinant value of the matrix A.
adjoint-matrix(matrix A) - function finds and return adjoint matrix of the matrix A.
Read matrix A
D = determinant(matrix A)
IF D== 0
print "matrix A is singular matrix"
print "and so matrix A is not invertable"
return
ELSE
matrix adjA = adjoint-matrix(matrix A)
matrix A-1 = 1 /D * ( adjA )
END
print A-1
Matrix Determinant Adjoint Inverse - Java program
The Java program class has the following 3 static membership function to finds determinant value of a matrix 3x3 and adjoint of a matrix 3x3 and inverse of a matrix 3x3.
The three static membership functions are
- determinant - The function/method which takes a matrix object as an argument, finds determinant of the matrix and returns determinant value as the execution result.
- adjmatrix - The function/method which takes a matrix object as an argument, finds adjoint of the matrix and returns an adjoint matrix object as the execution result.
- inverse - The function/method which takes a matrix object as an argument, finds inverse matrix of the matrix and returns an inverse matrix object as the execution result.
public class MatrixOpr2 {
public static double determinant(Matrix mat)
{
double det=0;
double M[] = new double[mat.getNcol()];
for(int c=0;c<mat.getNcol();c++)
{
Matrix cmat=mat.cofactor(0, c);
M[c] =(cmat.getElement(0,0)* cmat.getElement(1,1) -
cmat.getElement(0,1)* cmat.getElement(1,0)) ;
}
int r=0;
for(int c=0;c<mat.getNcol();c++)
det = det + Math.pow(-1, c+r)*mat.getElement(r, c) * M[c];
return det;
}
public static Matrix adjmatrix(Matrix mat)
{
Matrix adjmat =new Matrix(mat.getNrow(),mat.getNcol());
for(int r=0;r<mat.getNrow();r++)
{
for(int c=0;c<mat.getNcol();c++)
{
Matrix cmat=mat.cofactor(r, c);
double val= Math.pow(-1, c+r)
* ( cmat.getElement(0,0)* cmat.getElement(1,1)
- cmat.getElement(0,1)* cmat.getElement(1,0)) );
adjmat.setElement(r, c, val);
}
}
return adjmat;
}
public static Matrix inverse(Matrix mat)
{
double det=MatrixOpr2.determinant(mat);
Matrix adj=MatrixOpr2.adjmatrix(mat);
Matrix tadj=adj.transpose();
Matrix imat= Scalar.divide(tadj, det);
return imat;
}
public static void main(String[] args)
{
double val[][]={{3,1,2},{2,-1,1},{1,3,-1}};
Matrix A=new Matrix(val);
System.out.println("Input Matrx :");
System.out.println(A.toString());
double det=MatrixOpr2.determinant(A);
System.out.println("Determinant of Matrix A");
System.out.println(det);
if (det==0) {
System.out.println(" Matrix A is singular ");
return;
}
Matrix adjmat=MatrixOpr2.adjmatrix(A);
System.out.println("nAdjoint Matrix of A :");
System.out.println(adjmat.toString());
Matrix Ai=MatrixOpr2.inverse(A);
System.out.println("nInverse Matrix of A:");
System.out.println(Ai.toString());
Matrix A2=MatrixOpr2.inverse(Ai);
System.out.println("nInverse Matrix of A1 =A :");
System.out.println(A2.toString());
Matrix I=MatrixOpr.multiply(A, Ai);
System.out.println("nIdentity Matrix : AA1=I");
System.out.println(I.toString());
}
}
Matrix Determinant Adjoint Inverse - Java program Output
Input Matrix A 3.0 1.0 2.0 2.0 -1.0 1.0 1.0 3.0 -1.0 Determinant of Matrix A 11.0 Adjoint of Matrix A -2.0 3.0 7.0 7.0 -5.0 -8.0 3.0 1.0 -5.0 Inverse Matrix of A -0.18181818181818182 0.6363636363636364 0.2727272727272727 0.2727272727272727 -0.45454545454545453 0.09090909090909091 0.6363636363636364 -0.7272727272727273 -0.45454545454545453 Prove that (A-1)-1= A Inverse Matrix of A-1 2.9999999999999996 1.0 2.0 2.0 -0.9999999999999997 0.9999999999999999 1.0 2.9999999999999996 -0.9999999999999997 Prove that AA-1=I Identity Matrix I 1.0 0.0 0.0 0.0 1.0 -5.551115123125783E-17 -1.1102230246251565E-16 1.1102230246251565E-16 1.0
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