import java.util.Scanner;
public class Exercise07_23 {
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
System.out.print("Enter a11, a12, a13, a21, a22, a23, a31, a32, a33: ");
double[][] A = new double[3][3];
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
A[i][j] = input.nextDouble();
double[][] inverseOfA = inverse(A);
printMatrix(inverseOfA);
}
public static void printMatrix(double[][] m) {
// ????
}
public static double[][] inverse(double[][] A) {
double[][] result = new double[A.length][A.length];
// Compute |A|
double determinantOfA = 1; // A[0][0] * A[1][1] * A[2][2] * ...;
result[0][0] = (A[1][1] * A[2][2] - A[1][2] * A[2][1]) / determinantOfA;
result[0][1] = 1; // ??
result[0][2] = 1; // ??
result[1][0] = 1; // ??
return result;
}
}
You basically write a nested for loop (one for within another one), to copy the elements of the matrix to a new matrix.
A c program is also known as a computer program. A singular matrix has no inverse. An equation to determine this would be a/c=f. <<>> The determinant of a singular matix is zero.
A number of well-tested open-source Matrix Java libraries are available. Best to find and use one that's been around for a while since most of the bugs have been worked out. If you need to write your own it's still worth-while to examine the APIs of those libraries first.JAMA is a free Java library for basic linear algebra and matrix operations developed as a straightforward public-domain reference implementation by MathWorks and NIST.Example of Use. The following simple example solves a 3x3 linear system Ax=b and computes the norm of the residual.double[][] array = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};Matrix A = new Matrix(array);Matrix b = Matrix.random(3,1);Matrix x = A.solve(b);Matrix Residual = A.times(x).minus(b);double rnorm = Residual.normInf();
Automated proofs are a complicated subject. If you are not an expert on the subject, all you can hope for is to write a program where you can input a sample matrix (or that randomly generates one), and verifies the proposition for this particular case. If the proposition is confirmed in several cases, this makes the proposition plausible, but is by no means a formal proof.Better try to prove it without writing any program.Note: it is not even true; it is the inverse of the matrix which gives identity when is multiplied with the original matrix.
The inverse of resistance is conductance.
(I-A)-1 is the Leontief inverse matrix of matrix A (nxn; non-singular).
Let A by an nxn non-singular matrix, then A-1 is the inverse of A. Now (A-1 )-1 =A So the answer is yes.
If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
No. A square matrix has an inverse if and only if its determinant is nonzero.
From Wolfram MathWorld: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that AA-1=I where I is the identity matrix.
it is used to find the inverse of the matrix. inverse(A)= (adj A)/ mod det A
The fact that the matrix does not have an inverse does not necessarily mean that none of the variables can be found.
That is called an inverse matrix
A rectangular (non-square) matrix.
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link.www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdfSince (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link.www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdfSince (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link.www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdfSince (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.