Các phép toán ma trận thường gặp

int[][] AddMatrices(int[][] a, int[][] b)
{
    int rows = a.Length;
    int[][] result = new int[rows][];
    
    for (int i = 0; i < rows; i++)
    {
        result[i] = new int[a[i].Length];
        for (int j = 0; j < a[i].Length; j++)
        {
            result[i][j] = a[i][j] + b[i][j];
        }
    }
    return result;
}

int[][] Transpose(int[][] matrix)
{
    int rows = matrix.Length;
    int cols = matrix[0].Length;
    
    int[][] result = new int[cols][];
    for (int i = 0; i < cols; i++)
    {
        result[i] = new int[rows];
        for (int j = 0; j < rows; j++)
        {
            result[i][j] = matrix[j][i];
        }
    }
    return result;
}

int[] RowSums(int[][] matrix)
{
    int rows = matrix.Length;
    int[] sums = new int[rows];
    
    for (int i = 0; i < rows; i++)
    {
        int sum = 0;
        for (int j = 0; j < matrix[i].Length; j++)
        {
            sum += matrix[i][j];
        }
        sums[i] = sum;
    }
    return sums;
}

int[][] MultiplyMatrices(int[][] a, int[][] b)
{
    int rows = a.Length;
    int cols = b[0].Length;
    int inner = b.Length;
    
    int[][] result = new int[rows][];
    for (int i = 0; i < rows; i++)
    {
        result[i] = new int[cols];
        for (int j = 0; j < cols; j++)
        {
            int sum = 0;
            for (int k = 0; k < inner; k++)
            {
                sum += a[i][k] * b[k][j];
            }
            result[i][j] = sum;
        }
    }
    return result;
}