7.87 For the grid shown in the figure with positive and negative signs, the following operation is allowed: change all the signs in a certain row or column to the opposite of their original signs, and after each operation, record the absolute value of the difference in the number of the two types of signs. Try to find the minimum value among all such absolute values.

Allow for the operation: change all the signs in a certain row or column to the opposite of their original signs, and after each operation, record the absolute value of the difference in the number of the two types of signs. Try to find the minimum value among all such absolute values.
[Solution] Because with each operation, the number of positive signs in the row or column changes by an even number, the parity of the number of positive signs in the grid remains unchanged throughout the operations. Since the original table has 37 positive signs, there will always be an odd number of positive signs in the table. Therefore, the difference in the number of the two types of signs in the table is a non-zero even number, and its absolute value is of course no less than 2.

On the other hand, when the first operation changes the signs in the first row from the top, and the second operation changes the signs in the first column from the right, the table will have 31 positive signs and 33 negative signs, with the absolute value of the difference in their numbers being 2.
Thus, the minimum value sought is 2.