A fine summary. Another Matilda who had even more influence was Matilda of Canossa. The classic book on her life is Michèle Spike, Tuscan Countess, (Penguin). Here is a description:

https://www.finestresullarte.info/en/works-and-artists/the-life-of-an-extraordinary-woman-matilda-of-canossa-her-castles-her-places