以下是一个示例代码，通过比较每个列中的值与其旁边的列中的值来解决问题：

def compare_adjacent_columns(matrix):
    rows = len(matrix)
    cols = len(matrix[0])
    
    for row in range(rows):
        for col in range(cols-1):
            if matrix[row][col] > matrix[row][col+1]:
                print(f"Value at ({row}, {col}) is greater than value at ({row}, {col+1})")
            elif matrix[row][col] < matrix[row][col+1]:
                print(f"Value at ({row}, {col}) is less than value at ({row}, {col+1})")
            else:
                print(f"Value at ({row}, {col}) is equal to value at ({row}, {col+1})")

# 示例矩阵
matrix = [[1, 2, 3],
          [4, 5, 6],
          [7, 8, 9]]

compare_adjacent_columns(matrix)

输出结果为：

Value at (0, 0) is less than value at (0, 1)
Value at (0, 1) is less than value at (0, 2)
Value at (1, 0) is less than value at (1, 1)
Value at (1, 1) is less than value at (1, 2)
Value at (2, 0) is less than value at (2, 1)
Value at (2, 1) is less than value at (2, 2)

以上示例代码会遍历矩阵的每一行，比较当前列的值与下一列的值，然后根据比较结果输出相应的信息。在这个示例中，我们只是简单地打印了比较结果，你可以根据实际需求进行进一步的操作。