Notation for image and kernel capitalization of first letter

In the mathematical notation for image and kernel one usually writes $\ker$ for kernel and $\DeclareMathOperator{\img}{Im}\img$ for image. Why is the "k" small but the "I" big?

• I do not capitalize $\text{im}$. – Git Gud Mar 12 '15 at 22:13
• I don't capitalize $\text{im}$ either. Some people capitalize $\text{Ker}$, even. It's a wild world out there. – Qiaochu Yuan Mar 12 '15 at 22:15
• There is no uniform notation: both are capitalised in French. – Bernard Mar 12 '15 at 22:24
• I don't capitalize either , since $Im$ can refer to an imaginary part – krirkrirk Mar 12 '15 at 22:26
• ok great thanks for the comments. I will write both small then :) – Loreno Heer Mar 12 '15 at 22:49