A feminist perspective would study the actions of the female character by connecting them to the social, political and economic conditions of women at the time.
A feminist reading of Queen Gertrude would focus on her role as queen and mother, but also as a woman in Elizabethan times. We learn that Queen Gertrude has married her husband's brother shortly after her husband's death. However, she does not explain why she does so. In fact, the Queen speaks very little in the play, and this means we often have to guess her motivations and preferences. It is possible that the Queen believed marriage would keep her and the kingdom safe. Moreover, she most likely felt like she had few choices besides remarrying if she wanted to continue to be a Queen.
The Queen's choices are also complicated by the fact that she is a mother. Hamlet feels betrayed because of her marriage, and he often complains and insults her because of her decision. This shows that Hamlet feels personally affected by the Queen's choice of husband. This is a common idea at the time, when women's choices and sexuality were considered to be strongly connected to her male relatives, and not only to herself.