VECTOR SPACES - LINEAR ALGEBRA

We introduce vector spaces in linear algebra.

#LinearAlgebra #Vectors #AbstractAlgebra

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#LinearAlgebra #Algebra #UniversityMath #Lecture

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In this video we talk about Vector Spaces and ask ourselves if some sets are vector spaces. We also talk about the polynomial vector space.

Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[nirupamayyagari]

Ive been told so much that linear algebra focuses more on visualizing the actual spaces rather than functions. Ive watched videos and read material and somewhat understood it, but your drawings and this video and the functions you chose made that make so much more sense.

[beedlejeedle]

dude you have no idea how much the visual representation helped; why my prof never explained this visually is beyond me

[jared]

Helpful video. I was having a little trouble with this concept but your explanation and visuals were just what I needed.

[andrewburnette]

So far the best explanation on proving vector spaces.

[meensbeans_]

Thanks for this, I just started Vector Spaces and since I haven’t seen any examples of questions I wasn’t sure how it’s tested. I’m assuming the whole section is tested by proofs.

[Nini-vwzn]

Bruh, 5 minutes in, and I've already gained a clearer understanding of vector spaces than I ever did from attending a lecture and reading the syllabus

[mardhiahmichael]

Im crying because i dont understand vector space 😭😭😭😭😭😭. Why do i major in math, i can't even do this simple stuff😭😭😭😭😭

[lm]

Great video. Just one small note if I may - the non-integer (7/2) exponent in the example at 08:40 makes it a non-polynomial.

[happygohil]

here set of polynomial of degree <=n will be the vector space because for An+Bn=0 axiom 1 will not satisfy
axiom 1(u and v in V then u+v in V)
is my point is valide?

[johnaiii]

starting at 7:48 I don't get it, how do I turn from polynomial to a vector(with corresponding value for each coordinate or each dimension value)? 'cause vectors has a n x 1 size(n rows, 1 column). pls help

[lalith_kumar_akhila]

Excellent Explanation is an understatement..no words...thanks a ton

[Nohope__]

Professor Strang's linear algebra teaches you, 3Blue1Brown essence of linear algebra shows you, and then this channel saves you.

[kathyw.]

You can't have a non-integer exponent on the variable, in a polynomial. I think a zero degree polynomial would just mean the exponent was 0, so it could be a constant other than 0.

[chillsway]

Thank you for saving my final exam with this now I can get an A

[mahimapareek]

Please share the link of your previous videos where you proved all these.

[hyderfocus]

For the problem at 6:00, saying that if u=(-1, 2) and (-1)(2) is not >= 0, this would be false right? As we cannot use a vector that is itself not in the W set?

[AsparagusSucks]

TYSM this is what I needed. A visual and slow explanation. My UNI just rushed through the basic concepts leaving me super confused.

[jyc]

thank u for such a good lecture. i have a quick question, in polynomials, what if scalar is zero? is it still in the vector?

[Christian-mndh]

11:03 how is closure under addition satisfied? what if u + v = p(t) + (-p(t)) ?? that would be the 0 polynomial. confused

[sharonbell]

a very difficult topic for me became clear, thank you!