用java声明Matrix类表示矩阵，使用二维数组存储矩阵元素，实现以下方法：

public class Matrix {
private static String matrix_A;
private int mx[][], m, n;
public Matrix(int r, int c) {
m = r;
n = c;
mx = new int[m][n];
iniMatrix();
}
public Matrix() {
m = 3;
n = 3;
mx = new int[3][3];
iniMatrix();
}
public void iniMatrix()// 随机取数
{
int i, j;
for (i = 0; i <= m - 1; i++)
for (j = 0; j <= n - 1; j++)
mx[i][j] = (int) (Math.random() * 100);
}
public void tranMatrix()// 转置矩阵
{
int i, j, t;
int mt[][] = new int[m][n];
for (i = 0; i <= m - 1; i++)
for (j = 0; j <= n - 1; j++)
mt[i][j] = mx[i][j];
t = m;
m = n;
n = t;
mx = new int[m][n];
for (i = 0; i <= m - 1; i++)
for (j = 0; j <= n - 1; j++)
mx[i][j] = mt[j][i];
}
public void printMatrix()// 输出矩阵所有值
{
int i, j;
for (i = 0; i <= m - 1; i++) {
for (j = 0; j <= n - 1; j++)
System.out.print(" " + mx[i][j]);
System.out.println();
}
}
//判断一个矩阵是否为上三角矩阵
public boolean isUpperTriangularMatrix() {
int i, j = 0;
int c = this.mx[1][0];

for(i=1; ifor(j=0; jif(this.mx[i][j] != c)
break;
if(i>=this.mx.length)
return true;
return false;
}
public void addMatrix(Matrix b)// 矩阵相加
{
int i, j;
for (i = 0; i <= m - 1; i++)
for (j = 0; j <= n - 1; j++)
mx[i][j] = mx[i][j] + b.mx[i][j];
}
public static void main(String args[]) {
Matrix ma = new Matrix(4, 3);
Matrix mb = new Matrix(4, 3);
System.out.println("The matrix_A:");
ma.printMatrix();
System.out.println("The matrix_B:");
mb.printMatrix();
if(ma.isUpperTriangularMatrix())
System.out.println("上三角矩阵：\n" + ma.isUpperTriangularMatrix());
System.out.println("Matrix_A + Matrix_B:");
ma.addMatrix(mb);
ma.printMatrix();
System.out.println("Transpose Matrix_A:");
mb.tranMatrix();
mb.printMatrix();
System.out.println("Transpose Matrix_A+Matrix_B:");
mb.tranMatrix();
mb.printMatrix();
}
}

我简单的叙述下，matrix就一个二维数组，矩阵的转置就是对角上的折叠，说白了就是两个值的互换]。求和就非常简单了，必须是行和列都相同的才行，把对应位置的值加起来就ok。转置的具体方式可参考线性代数里的介绍