I am not sure whether I can simply not find an answer or I am just missing something obvious, but there is a step in the Hungarian algorithm which I am having trouble understanding; I will be referencing the algorithm as stated on the Wikipedia page on the topic.
I perfectly understand why Step 1 results in an equivalent problem, where the optimal solution remains the same, but when it comes to the adjustment step (Step 5) I get confused.
Find the lowest uncovered value. Subtract this from every unmarked element and add it to every element covered by two lines.
This is equivalent to subtracting a number from all rows which are not covered and adding the same number to all columns which are covered. These operations do not change optimal assignments.
Why does this step not change the optimal assignments? Is there an intuitive explanation for this?