Is Hamlet Mad?

Throughout the play, Hamlet's actions have long been debated. Is he mad or are his actions justified? In my own opinion, I believe that his actions are triggered by specific events from his past, specifically, the fact that Hamlet's uncle murdered his father. However, after much thought regarding Hamlet's character, I think it is equally important to analyze how a human chooses to handle themselves when specific problems arise throughout a lifetime. While I believe "mad" might have a more negative connotation, I do believe we as readers/watchers can categorize Hamlet as a man who has mental instability.  It is evident that throughout the play, there are several instances where this mental instability is expressed. For example, when Hamlet fully discovers that his uncle Claudius murders his father. Losing a loved one impacts a person in ways unimaginable. Moreover, to have his mother re-marry his father's murderer could easily put him over the edge. Hamlets "madness" is displayed fully in the scene where Hamlet explains angrily to his mother the wrongdoings of Claudius. Because she reacted with fear, Polonius's call out for help from the curtain ultimately startles Hamlet enough to kill him with his sword. This specific action of killing Polonius specifically builds on the point that Hamlet is mad because he murdered a man without even knowing who he was (since he was hidden behind a curtain). Aside from this scene, his contemplation of life and death is another reason why we see that Hamlet is mad. Throughout his "To be or not to be" speech we gather that Hamlet debates committing suicide. Hamlet feels as though no one is listening to the truth he speaks, and I agree that if an entire population (including family) completely turned on me, I might be more likely to lash out just like Hamlet. For these reasons, I believe that while he most definitely is "mad" I can understand (to some extent) why he may act this way.