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Vector Spaces Explained | Linear Algebra
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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
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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Thanks to Loke Tan, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon!
Outro music is mine. You cannot find it anywhere, for now.
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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
◉Textbooks I Like◉
★DONATE★
Thanks to Loke Tan, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon!
Outro music is mine. You cannot find it anywhere, for now.
Follow Wrath of Math on...
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