The Oxford Concise Dictionary of Literary Terms (OCDLT) and Arthur Miller both define a tragic hero as a character in a play or drama, most likely the protagonist, who is made victim to a circumstance within the plot. To this extent, Arthur Miller's definition of a tragic hero varies because he believes "the common man is as apt a subject for tragedy in its highest sense as kings were [and] the tragic feeling is evoked in us when we are in the presence of a character who is ready to lay down his life, if need be, to secure one thinghis sense of personal dignity" (Miller, 1633), meaning that mankind keeps tragedy above all forms because they are given the same mental abilities as the nobles and you do not have to be of nobility to be a tragic hero.
Tragic heroes bring about a tragedy by suffering from a situation, making it a tragedy. The OCDLT defines tragedy as a play "representing the disastrous downfall of a central character, the protagonist" (Baldick, 260), meaning that tragic heroes are endowed with a tragic flaw and doomed to make a serious error in judgment. Furthermore, heroic drama is defined as "the noble hero would typically be caught in a conflict between love and patriotic duty, leading to emotional scenes presented in a manner close to opera" (Baldick, 112-113), implying that the hero is of nobility.
Drawing from these definitions, in Miller's "Death of a Salesman", Willy Lowman would not be considered a tragic hero because he is a common man, who was not born into nobility. He tries to provide for his family but fails to live up to the standards of being a tragic hero because he never accepts or admits to his own errors. In Sophocles's "Oedipus the King", Oedipus was of nobility and therefore would be considered a tragic hero. I don't see Willy Lowman as a tragic hero because he was not a victim of fate. Willy determined his own destiny when he decided to commit adultery, losing all the respect from his son