Minor of a matrix

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.

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

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;
}

Quote:

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Originally Posted by 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;
}

---

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:

Code:

---

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

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

Code:

---

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;
        }
}

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

Code:

---

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:

Code:

---

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();
                }
        }
}

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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