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Dimension of a Vector Space | Linear Algebra
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We define the dimension of a vector space by first looking at some important facts concerning the number of vectors in a basis for a vector space. We then see some familiar examples of vector spaces and their dimensions, including R^n, Pn, and Mmn, and finish by finding the dimension of the solution space of a homogenous linear system. #linearalgebra
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0:00 Intro
1:23 All Bases have the Same Number of Vectors
2:04 Definition of Dimension
2:40 Examples in Familiar Vector Spaces
5:00 Dimension of a Solution Space
8:30 Conclusion
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Thanks to Loke Tan, Raül Beienheimer, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, 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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Join Wrath of Math to get exclusive videos, music, and more:
0:00 Intro
1:23 All Bases have the Same Number of Vectors
2:04 Definition of Dimension
2:40 Examples in Familiar Vector Spaces
5:00 Dimension of a Solution Space
8:30 Conclusion
◉Textbooks I Like◉
★DONATE★
Thanks to Loke Tan, Raül Beienheimer, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, 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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