Minor of a matrix

[sehudson]

I have a 4x4 matrix that I need to find the minor of.

4 5 6 2
3 4 5 5
7 4 3 3
5 7 6 8

The minor is basically the resultant matrix that you get when you remove the row/column that [i,j] is in. So for instance, if I had a Matrix(A), and I needed the minor of A[2,3], I would be removing (from the above) I would end up with the following matrix:

4 5 6
3 4 5
5 7 6


Any ideas on how I could get that result? Preferably something where I could pass in the 2d array representing the matrix, and the i,j position that I wanted to eliminate.

[JosAH]

Why do you need to find the minor of a matrix? Do you want to find the determinant of a matrix? There are better ways ...

kind regards,

Jos

[sehudson]

yes, the assignment is to recursively find the determinant of a matrix, preferably using the minor. so its something like

public double FindDeterminant(double[][] inputMatrix){
double determinant = 0;
//logic

return determinant;
}

[JosAH]

yes, the assignment is to recursively find the determinant of a matrix, preferably using the minor. so its something like

public double FindDeterminant(double[][] inputMatrix){
double determinant = 0;
//logic

return determinant;
}

If you really have to use the minors of a matrix I'd use 'views' on the matrix; here's how: first define an interface:

interface MatrixView {
	double get(int i, int j);
	int dim();
}

This doesn't say much but here's a RawMatrixView that offers a 1 to 1 view of a raw matrix:

class RawMatrixView implements MatrixView {
	private double[][] mat;
	
	public RawMatrixView(double[][] mat) {
		this.mat= mat;
	}
	
	public double get(int i, int j) {
		return mat[i][j];
	}
	
	public int dim() {
		return mat.length;
	}
}

This doesn't say much either but given this first class we can build a MinorMatrixView:

class MinorMatrixView implements MatrixView {
	MatrixView mv;
	int r, c;
	
	MinorMatrixView(MatrixView mv, int r, int c) {
		this.mv= mv;
		this.r= r;
		this.c= c;
	}
	
	public double get(int i, int j) {
		if (i >= r) i++;
		if (j >= c) j++;
		return mv.get(i, j);	
	}
	
	public int dim() {
		return mv.dim()-1;
	}
}

As you can see from this class if a row or column element is refered it simply returns the element in the next row or column. And, more important all MatrixView objects can be wrapped by others allowing for a recursive approach (needed by your determinant finding method).

Here's a small class that tests the entire thing:

public class T {
	public static void main(String[] args) {
		double[][] mat= { 
				{ 1, 2, 3, 4 },
			    { 2, 3, 4, 5 },
			    { 3, 4, 5, 6 },
			    { 4, 5, 6, 7 }
		};
		
		MatrixView rmv= new RawMatrixView(mat);
		MinorMatrixView mmv= new MinorMatrixView(rmv, 1, 2);
		
		for (int i= 0; i < mmv.dim(); i++) {
			for (int j= 0; j < mmv.dim(); j++)
				System.out.print(mmv.get(i, j)+" ");
			System.out.println();
		}
	}
}

This class builds a minor (ignore row 1, column 2) of a raw matrix. I think you can take it from here.

kind regards,

Jos