Gertrude's personality in Hamlet is one of the most interesting aspects of the play and Gertrude herself is one of the more complex characters in the play. Critics of Hamlet have long debated Gertrude's personality and her feelings about her dead husband, her new husband and her son. Throughout the play, there's a question as to how deeply involve in King Hamlet's murder Gertrude was. While at the end of the play she appears ignorant of the crime, some critics have argued that she was, in some way, involved in the plot to kill King Hamlet. Shakespeare never tells us this for certain, though, which gives Gertrude’s character a measure of ambiguity.
In terms of her personality, some critics feel that Gertrude is closely attached to and highly dependent upon Claudius and is at his mercy throughout the play. A number of critics feel that she is either helpless against Claudius or simply weak willed. Hamlet himself suggests that Gertrude is motivated by sexual desire for Claudius, a point which some critics believe to be true.
On the other hand, some other critics view Gertrude as being a caring mother who is worried about her son's sanity and well being. Also, her love for Claudius is seen by some critics as being deep and true and not a result of mere sexual passion. Critics who defend Gertrude's character also point to her self-awareness, especially in act three, scene four of the play, in which she seems to admit feeling remorse for her behavior.
Throughout the play, Gertrude seems to be stuck between Claudius and Hamlet and unable to choose which of the two to side with. She does not abandon her husband but, also, she does not reveal her son's suspicions to her husband.
All and all, Gertrude’s personality is complicated. On one hand she seems helpless, weak spirited and motivated by desire. On the other hand she can also be seen as being intelligent, self-aware and motivated by love for both her son and her new husband.