Java扩充例题4.14的功能，实现两个矩阵的相加、减等；Java封装一个类MatrixLocation

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第六题

所有矩阵的题目用二维数组实现都很简单，只有矩阵的逆比较麻烦，具体代码如下（建议从上边直接下载源代码，包含更多的注释和解释）

主类

import cn.com.my.Matrix;

public class Test {
    public static void main(String[] args) {
        int[][] matrix1 = {{2, 3, 4}, {5, 6, 7}};
        int[][] matrix2 = {{1, 2}, {3, 4}};
        int[][] matrix5 = {{1, 2}, {-1, -3}};
        int[][] matrix11 = {{1, 2, 3}, {4, 5, 6}};
        int[][] matrix3 = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
        int[][] matrix4 = {{1, 2, -1}, {3, 1, 0}, {-1, -1, -2}};
        Matrix matrixMultiplication = new Matrix();
        int[][] matrixMultiply = matrixMultiplication.matrixMultiply(matrix1, matrix2); 
        matrixMultiplication.printMatrix(matrixMultiply);
        int[][] matrixAddition = matrixMultiplication.matrixAddition(matrix1, matrix11); 
        matrixMultiplication.printMatrix(matrixAddition);
        int[][] matrixSubtraction = matrixMultiplication.matrixSubtraction(matrix1, matrix11); 
        matrixMultiplication.printMatrix(matrixSubtraction);
        int[][] matrixTranspose = matrixMultiplication.matrixTranspose(matrix1); 
        matrixMultiplication.printMatrix(matrixTranspose);
        int[][] matrixInverse = matrixMultiplication.matrixInverse(matrix5);
        matrixMultiplication.printMatrix(matrixInverse);

    }
}

Matrix类

package cn.com.my;

public class Matrix {
    public int[][] matrixMultiply(int[][] a, int[][] b) {
        if (a[0].length != b.length) {
            return null;
        }
        int[][] c = new int[a.length][b[0].length];
        for (int i = 0; i < a.length; i++) {
            for (int j = 0; j < b[0].length; j++) {
                for (int k = 0; k < a[0].length; k++)
                    c[i][j] += b[k][j] * a[i][k];
            }
        }
        return c;
    }

    public int[][] matrixAddition(int[][] a, int[][] b) {
        if (a[0].length != b[0].length || a.length != b.length) {
            return null;
        }
        int[][] c = new int[a.length][a[0].length];
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                c[i][j] = a[i][j] + b[i][j];
        return c;
    }

    public int[][] matrixSubtraction(int[][] a, int[][] b) {
        if (a[0].length != b[0].length || a.length != b.length) {
            return null;
        }
        int[][] c = new int[a.length][a[0].length];
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                c[i][j] = a[i][j] - b[i][j];
        return c;
    }

    public int matrixMinor(int[][] a,int i,int j) { 
        int[][] c = new int[a.length-1][a.length-1];
        int b = 0;
        if (a.length != a[0].length) {
            return 0;
        } else if (a.length == 1) {
            return 0;
        } else {
            for (int i1 = 0; i1 < a.length; i1++) {
                for (int j1 = 0, j2 = 0; j1 < a.length - 1; j1++, j2++) {
                    for (int k1 = 0, k2 = 0; k1 < a[0].length - 1; k1++, k2++) {
                        if (j2 == i)
                            j2++;
                        if (k2 == j)
                            k2++;
                        c[j1][k1] = a[j2][k2];
                    }
                }
                b = determinant(c);
            }
            if((i+j)%2==1)
                return -b;
            else
                return b;
        }
    }
    public int determinant(int[][] a){ 
        int[] b=new int[a.length];
        int[][] c=new int[a.length-1][a[0].length-1];
        int sum=0;
        if (a.length != a[0].length) {
            return 0;
        } else if (a.length == 1) {
            return a[0][0];
        }else if (a.length == 2){
            return (a[0][0]*a[1][1])-(a[0][1]*a[1][0]);
        }else {
            for (int i = 0;i < a.length;i++){
                for (int j1 = 0,j2 = 1;j1 < a.length-1;j1++,j2++){
                    for (int k1 = 0,k2 = 0;k1 < a[0].length-1;k1++,k2++) {
                        if(k2 == i)
                            k2++;
                        c[j1][k1]=a[j2][k2];
                    }
                }
                b[i]=a[0][i]*determinant(c);
                if (i%2 == 1)
                    sum -= b[i];
                else
                    sum += b[i];
            }
            return sum;
        }
    }
    public int[][] matrixAdjugate(int[][] a){  
        int[][] c = new int[a.length][a[0].length];
        for (int i = 0; i < a.length; i++){
            for (int j = 0; j < a[i].length; j++){
                c[i][j] = matrixMinor(a, j, i);
            }
        }
        return c;
    }


    public int[][] matrixInverse(int[][] a){ 
        if(a.length != a[0].length)
            return null;
        int[][] c = new int[a.length][a[0].length];
        int[][] d = new int[a.length][a[0].length];
        int b = determinant(a); 
        d=matrixAdjugate(a);
        if(b==0) {
            for (int i = 0; i < d.length; i++) {
                for (int j = 0; j < d[0].length; j++) {
                    c[i][j] = 0;
                }
            }
        }
        else{
            for (int i = 0;i < d.length;i++){
                for(int j = 0;j < d[0].length;j++){
                    c[i][j] = d[i][j] / b;
                }
            }
        }

        return c;
    }

    public int[][] matrixTranspose(int[][] a) { 
        int[][] c = new int[a[0].length][a.length];
        for (int i = 0; i < a[0].length; i++){
            for (int j = 0; j < a.length; j++){
                c[i][j] = a[j][i];
            }
        }
        return c;
    }

    public void printMatrix(int[][] c) {
        if (c != null) {
            for (int i = 0; i < c.length; i++) {
                for (int j = 0; j < c[0].length; j++) {
                    System.out.printf("%d ", c[i][j]);
                }
                System.out.println();
            }
        } else {
            System.out.println("无效");
        }
        System.out.println();
    }
}

第七题

主类

public class Test {
    public static void main(String[] args){
        MatrixLocation matrixLocation = new MatrixLocation();
        double[][] a = {{1.2,1.3,2.4},{2.1,5.2,6.2},{1.3,2.5,6.1}};
        matrixLocation.location(a);
    }
}

 MatrixLocation类

public class MatrixLocation {
    int row;
    int column;
    double maxValue=0;
    public void location(double[][] a){
        for (int i = 0; i < a.length; i++){
            for (int j = 0; j < a[0].length; j++){
                if (maxValue < a[i][j]){
                    maxValue = a[i][j];
                    row = i;
                    column = j;
                }
            }
        }
        System.out.println("最大值是："+maxValue);
        System.out.println("位置是："+"第"+row+"行"+"第"+column+"列");
    }

}