# Thread: Infinite Dimensional Vector Space

1. ## Infinite Dimensional Vector Space

Dear Members
Kindly guide me about Infinite Dimensional Vector Space? I am requested to give easy examples Infinite Dimensional Vector Space with proof.
Waiting for good response.

2. ## Re: Infinite Dimensional Vector Space

The space of polynomials over an infinite field (where the vectors are the coefficients of each power of x).
$\displaystyle \{0,1\}^\infty$ (each coordinate is either zero or one, and the addition is 0+0=1+1=0, 0+1=1+0=1). Over the field $\displaystyle \Bbb{F}_2$.
$\displaystyle \Bbb{R}^\infty$
The space of continuous functions $\displaystyle f:\Bbb{R}\to \Bbb{R}$
$\displaystyle \mathcal{L}^p$ spaces
The list goes on...

What sort of examples are you looking for. Try looking up Infinite Dimensional Vector Space examples.

3. ## Re: Infinite Dimensional Vector Space

Dear SlipEternal