Coordinate Vectors Relative to a Basis | Linear Algebra

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We introduce the definition of the coordinates of a vector relative to an arbitrary basis and the idea of a coordinate vector relative to a basis. Any vector v in a vector space V with basis S has a unique representation as a linear combination of the vectors in S, and the coefficients in this linear combination make up what we call the coordinates of v relative to the basis S. We will look at several examples of coordinate vectors and do an example of finding a coordinate vector relative to a nonstandard basis in R^3. #linearalgebra

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0:00 Intro
1:01 Two Important Facts
2:50 Definition of Coordinate Vector Relative to a Basis
4:30 Mapping to R^n
4:52 Notation
5:13 Examples in Pn
6:34 Example in M22
7:49 Find Coordinate Vector Relative to Nonstandard Basis in R^3
10:29 Find Vector with Given Coordinates
11:31 Conclusion

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Комментарии
Автор

Ok the timing couldn't be more impeccable looool. I was half a asleep for coordinate vectors in my Linear Algebra lecture today.

__Hmmmmmmmm__
Автор

These videos are a great basis for learning 😆👍

PunmasterSTP