Jadeite is a sodium aluminum pyroxene, formula NaAlSi2O6. It is monoclinic, but gem material is almost always a tough, interlocking aggregate rather than a single crystal. Hardness is about 6.5 to 7. The finest green is colored by chromium. Lavender, white, and black jadeite are the same mineral with different trace chemistry.
Nephrite is the other material historically called jade. It is an amphibole, not jadeite, and does not belong on this page. Imperial jade is a trade name for top green jadeite, not a separate species.