Minerva (Athena in Greek) was one of the most important of the ancient Greek & Roman goddesses. She was originally a Goddess of War, hence her armor & spear. Her role later expanded to Goddess of War, Trade, Wisdom & the Arts. (Those duties including Trade & War surely reflect modern economic motives.) She was fierce & brilliant. From 2C BC onwards, the Romans equated her with the Greek goddess Athena, Goddess of Music, Poetry, Medicine, Wisdom, Commerce, Weaving, Crafts, & Magic.
Christine Marie de France, Duchesse de Savoie (1606-1665) as Minerva with her son Francesco Hyacinte
Artists in the 15-18C sometimes painted their clients as allegories or personifications, & often painters would put the faces of their patrons or sponsors on the bodies of the saints. These came to be called donor portraits.
Allegorical portraits remained popular; & as time passed, they expanded to show the sitter as a goddess, or muse, or nymph in a rustic or garden setting. These allegories grew to include strong portraits of Minerva wearing idealized attire, nothing like the clothing worn by actual women of the period. Dressing scantily or provocatively would have been frowned upon if a proper lady was sitting for a realistic portrait, but if she were posing as an ancient goddess or muse, a little skin was acceptable.