Please forgive this physicist's thread :(adsbygoogle = window.adsbygoogle || []).push({});

I can define a Hilbert space that is :

1) [tex]\mathbb{R}^n[/tex] with the euclidian norm, especially on a real field, and which is finite dimensional : is it right ? This is the most stupid question ever.

2) over the quaternions [tex]\mathbb{H}[/tex] ?

3) if the dimension is infinite non-countable, it is not separable. There is no need to talk about topological or metrical separability, the two coincide.

Please some one answer. It is due to questions [thread=44301]here[/thread].

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hilbert space

**Physics Forums | Science Articles, Homework Help, Discussion**