Advanced Linear Algebra, Lecture 1.1: Vector spaces and linearity

Advanced Linear Algebra, Lecture 1.1: Vector spaces and linearity

The fundamental objects in linear algebra are vector spaces, which consist of a X of vectors closed under addition, subtraction, and scalar multiplication from a field K. Linear maps are structure preserving functions between vector spaces. In this lecture, we see the formal definitions and some examples of vector spaces and subspaces.

[juniorcyans]

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[MrTroywoo]

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[xoppa]

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[athelstanrex]

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[essadababneh]

I really wish you would upload videos on abstract algebra 2. it would be a life saver

[fsaldan]

A(v+w) is not equal to Av + Bw unless B = A, on 24'.

[Edia]

29:58 Does the function f satisfies f(x1)=a1, ..., f(xn)=an simultaneously?
How can describe set of basis in case of (iii)?
Thanks a lot!

[maxpercer]

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[marikoueno]

Thank you, professor! I am searching for such a video. Your visual group theory series is awesome, and I wanted to have group theory of vector space. Definitely, I will continue this course. Thank you!

[ammaralghamri]

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[marikoueno]

Thank you! Can I see your presentation slides as your visual group theory?

[paulwary]

Why the dual notation for the field, using both F and K?

[briannewman]

You stated that Z is not a Field because 0 does not have a multiplicative inverse. But, under Field, you said only that F\{0} must be an abelian group. The only thing you said requires a multiplicative inverse is a Group. You did not say that a Field must meet all the requirements of a Group.

[yuhao]

Hi, Prof. Thank you so much for sharing. Is there any way to get the slides? Thank you.

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