Eidolon

An eidolon (plural: eidola) (Greek: εἴδωλον 'image, idol, double, apparition, phantom, ghost') is a manifestation of the spirit of both a living or dead person. In contrast, a dead person's form in the underworld is called a skia.

Helen of Troy's eidolon is the most famous example. In one way it gives Helen life after death, but can also be seen as a product of her kleos (fame, renown). So when she appeared in Troy, she was never physically present in the city at all. Penelope encounters the eidola of the dead, constantly laboring against the eidolon of Klytamnestra and then later of Helen herself. Also after the death of the suitors, Theoklymenos notes that he sees the doorway of the court filled with their eidola.

Etymology
The Ancient Greek εἴδωλον (eídōlon, 'figure, representation') derives from εἶδος (eîdos, 'sight'), which is in turn from the verb εἴδω (eídō, 'I see'). Thus it could be said that the term describes the experience of seeing something that is not fully or not at all there. Ultimately from Proto-Indo-European *weyd- ('to know; see').