# Notation for DEs in Hilbert spaces

Look guys, I appreciate and understand that Hilbert are self-dual, but if you use two different notations for differentiation in a single equation when you could've used just one -- you got to really mean it.

Look at this:

Wherefore do you write so many symbols if could've written less and thus avoided being a liar? Take $\mathbb{R}^n$ for a Hilbert space in discussion, the left hand site is the derivative -- a row-vector ${^n}\mathbb{R}$, and the RHS is a column -- same derivative encoded as a vector.