ABSTRACT
The set of natural numbers {1, 2, 3, . . .} is denoted by N. The set of integers {. . . ,−2,−1, 0, 1, 2, . . .} is denoted by Z. Q denotes the set of rational numbers. Finally R and C denote the sets of real numbers and complex numbers, respectively. Observe that
N ⊂ Z ⊂ Q ⊂ R ⊂ C
The vector spaces encountered in physics are mostly real vector spaces and complex vector spaces. Classical mechanics and electrodynamics are formulated mainly in real vector spaces while quantum mechanics (and hence this book) is founded on complex vector spaces. In the rest of this chapter, we briefly summarize vector spaces and matrices (linear maps), taking applications to quantum mechanics into account.
