The term imperatrix seems not to have been used in Ancient Rome to indicate the consort of an imperator or later of an Emperor. In the early years of the Roman Empire there was no standard title or honorific for the Emperor's wife, even the "Augusta" honorific was rather exceptionally granted, and not exclusively to wives of living emperors.
It is not clear when the feminine form of the Latin term imperator originated or was used for the first time. It usually indicates a reigning monarch, and is thus used in the Latin version of titles of modern reigning Empresses.
Likewise, when Fortuna is qualified "imperatrix mundi" in the Carmina Burana there's no implication of any type of consort — the term describes (the Goddess or personified) Fortune "ruling the world".
In Christian context, Imperatrix became a laudatory address to the Virgin Mary, in diverse forms at least since the Middle Ages — for example, she is sometimes called "Imperatrix angelorum" ("regnant of the angels").
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