We introduce the definition of a vector space, consisting of the 10 vector space axioms. We'll see examples of vector spaces and nonexamples of vector spaces and prove some of the vector spaces are indeed vector spaces. We finish by looking at some basic properties of vector spaces. #linearalgebra
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0:00 Intro
0:42 Definition of a Vector Space
5:00 Example 1 (Zero Vector Space)
6:11 Example 2 (R^n)
6:58 Nonexample 1
7:50 Example 3 (Matrix Space)
9:32 Nonexample 2
11:05 Example 4 (Weird One)
15:33 Vector Space Properties
16:48 Basic Vector Space Properties
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