Aristotle was said that a tragic hero was a person that was more noble than evil, but experiences a change in fortune from good to bad. Brutus from the play "Julius Caesar" is a perfect example of a tragic hero. He is a noble person that does some horrific acts but still commits suicide in the end because of the death of his brother, his wife, and eventual defeat in the battle between his, and Cassius's armies, against Antony's and Octavius' armies. Brutus is a noble person because he is literally from noble blood and is a person of great importance in the eyes of the Romans; also he is a very trusted member of the Roman society.
However in Brutus's life he has made many fatal flaws the most significant of course being killing Caesar himself, but Brutus does this for noble causes to save the Roman people from lives of service to the evil Julius Caesar. Another flaw that doesn't make Brutus evil but does play a role in Brutus's death is letting the evil backstabbing Mark Antony live after Brutus and the others kill Caesar. Antony is the one that turns all the other Romans against Brutus and the other assassins.
This being said I do believe that Brutus's noble acts make up for him malicious acts, because Brutus had no intentions of upsetting or offending anyone when he killed Caesar, he only wanted what he thought would be best for the Roman population. Therefore Brutus is a nobler person than an evil person. As for his changing fortunes, Brutus goes from an all time high after killing Caesar to the lowest of lows because first his wife dies, then Brutus's brother in law kills himself after thinking that they have lost the battle against Antony and Octavius, then Brutus ends up killing himself because the deaths of his family members and his inevitable defeat in the battle.