notes / Studies in Algebra and Group Theory / chapter 2: Rings, Fields and Vector Spaces / From my notebooks
N14 ℝⁿ and ℂⁿ; Definition of Vector Space
FUN FACTS: 1777: Euler calls .
is our field and is either or . A number in the field scalar.
Definition N14.1 (List and length).
- A list is an ordered collection of elements.
- Its length is the number of elements in it.
A list of length is called an -tuple.
is the set of all lists of length of elements of .
Addition on as a vector space assigns an element to each pair of elements .
Scalar multiplication (SCALAR MULT OVER VECTOR) assigns an element to each and each :