ABSTRACT
In this chapter we study several useful constructions that yield a new vector space based on given ones. We also study how inner products and linear maps yield associated constructions.
Given vector spaces V1, . . . , Vk over the same field F, the Cartesian product vector space V1 × · · · × Vk is defined via
V1 × · · · × Vk = {
v1... vk
: vi ∈ Vi, i = 1, . . . , k}, v1...
