In the play, Gertrude is the mother of protagonist Hamlet and the Queen of Denmark. She is one of the most ambivalently interpreted literary characters.

When she is introduced in the play, she is already married to Claudius, brother to her first husband and now the King of Denmark. Hints given in the play of her character has been interpreted in different ages differently.

Since the beginning of the play, Gertrude’s concerns for Hamlet as a mother is obvious. At the same time, she also knows what she has done. She is conscious of her own flaws.

When contemplating on Hamlet’s possible source of madness, she doesn’t give in to the suggestion made by Polonius, rather she says that it must be “his father’s death and our o’erhasty marriage.” The conflict in her heart starts showing as the play progresses.

The way she deals with so courtly Polonius tells us of the essentiality in her character. She directs him to report in a way which has “more matter, with less art.” When all are eager to assign Ophelia’s rejection as the source of Hamlet’s madness, Gertrude hopes that Ophelia’s presence may correct his state of mind.

Traditionally, the flaw noted in her character is her lust which gives in to the seduction of Claudius so soon after her husband’s death but politically it can be hard for someone to remain queen and not marry the person who is to be the king. Hamlet sees her under the most negative light but in him one can see, as T. S. Eliot noted, “the effect of a mother’s guilt upon her son.”

Throughout the play, her silence towards the accusations made by Hamlet makes us think of her in a state of guilt. Hamlet and the ghost intermittently refer to Gertrude’s sexuality. There’s a hint at the matching of Claudius’ lust with Gertrude’s shameless sensuality.

She doesn’t care to answer to Hamlet but when he tells her that he’ll discover her true nature by setting up a mirror, she instantly reacts as if Hamlet is going to murder her.

In the later part of the play, Gertrude starts showing her emotional aspects. Her seemingly shallow coldness starts giving in to a realm of deeper personality. She says to Hamlet, “thou turn’st mine eyes into my very soul, and there I see such black and grained spots.”

Only when she comes to know that her husband was killed by Claudius, her conscience awakens. It proves that her conscience is more powerful than any carnal lust.

By the fifth act of the play, Gertrude is no more a passive character. Hamlet couldn’t kill Claudius earlier because, on some level, his will for revenge wasn’t greater than his wish to see his mother showing some guilt and moral upliftment.

Even when Claudius warns, Gertrude sips from the poisoned wine and before dying gives a final boost to Hamlet’s revenge against Claudius. In the end, her character comes out of passivity and in a sacrificial stint contributes towards the play’s tragic pinnacle.

Here are some important articles on Gertrude

https://www.bl.uk/shakespeare/articles/character-analysis-gertrude-in-hamlet