Robertson and Vincent on 1 Corinthians 11:7

Taken from Robertson's Word Pictures

The image and glory of God (εικων και δοχα τεου — eikōn kai doxa theou). Anarthrous substantives, but definite. Reference to Genesis 1:27 whereby man is made directly in the image (εικων — eikōn) of God. It is the moral likeness of God, not any bodily resemblance. Ellicott notes that man is the glory (δοχα — doxa) of God as the crown of creation and as endowed with sovereignty like God himself.

The glory of the man (δοχα ανδρος — doxa andros). Anarthrous also, man‘s glory. In Genesis 2:26 the lxx has αντρωπος — anthrōpos (Greek word for both male and female), not ανηρ — anēr (male) as here. But the woman (γυνη — gunē) was formed from the man (ανηρ — anēr) and this priority of the male (1 Corinthians 11:8) gives a certain superiority to the male. On the other hand, it is equally logical to argue that woman is the crown and climax of all creation, being the last.

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Next, we read in Vincent's Word Studies:

Image and glory (εἰκὼν καὶ δόξα)

For image, see on Revelation 13:14. Man represents God's authority by his position as the ruler of the woman. In the case of the woman, the word image is omitted, although she, like the man, is the image of God. Paul is expounding the relation of the woman, not to God, but to man.