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.
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.
Dear SlipEternal
Thanks for your kind guidance.