According to her Wikipedia article, she was the first wife of the Prince-Elector of Brandenburg, Joachim II Hector. He later married Jadwiga Jagiellonka of Poland.
From Wikimedia; spots and cracked paint flaws removed with Photoshop.
Magdalene’s hair appears to be encased in a coif. She wears a chignon, also encased in the caul or surrounded by bands. Her cape has fur-trimmed slits for her arms that are clad in tight sleeves adorned with wide cloth rings.
Keywords: 1529, Cranach the Elder, Magdalene von Sachsen, Prinzessin von Sachsen, Kurprinzessin von Brandenburg, Wettin family, Hohenzollern family, Princess, German, feathered brim hat, coif, chignon, under-bodice, chemise, high enclosing neckline, jeweled collar, pendant, bodice, jeweled trapezoidal neckline, long tapered sleeves, puffed cloth arm bands, jfur-trimmed cape, fur lapels, jeweled bodice ornament, vee neckline