This does what you want. Hopefully the variable and function names make it relatively clear what's going on.
list_of_strings = ['-1 -2 -3 -4 -5 -6 -7 -8 9 -10 11',' -17 18 19 20 -21 22 -23 ',' -36 -37 -38 39 40 41 42 -43 44 ']
def process(string_of_ints):
return ' '.join( str(-int(each_word)) for each_word in string_of_ints.split() )
result = [ process(each_string) for each_string in list_of_strings ]
print(result)
It can be collapsed into one line at the cost of some clarity:
result = [ ' '.join( str(-int(each_word)) for each_word in each_string.split() ) for each_string in list_of_strings ]
(NB: "invert" is really a potentially misleading word - in mathematics, when used unqualified, the most common interpretation means do 1/x, not -x; in computing it might mean any one of a number of different things, including reversing the order of a sequence).