Themes
Vector spaces, their functions and functionals
Related surveys
For info on linear maps on vector spaces, see that survey.
For numerical analysis, conditioning, stability, differnce equations, differential equations: see Numerical analysis ref.
Characterization of research effort
See linear algebra survey.
Interpretations and applications
Not necessarily just an abstraction of geometric 3-D or 2-D spaces. Many other things modelled by fixed length sequences of numbers.
Modelling the real world
A number can represent a weight, height etc.. It could mean a certain combination of weight, height etc..
Functions as vectors
Using coefficients
Take the polynomial
Using the domain
See function spaces section.