## VECTOR SPACES – LINEAR ALGEBRA

We introduce vector spaces in linear algebra.

#LinearAlgebra #Vectors #AbstractAlgebra

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Linear Algebra and Its Applications (Lay): https://amzn.to/37gBZ27
Linear Algebra Done Right (Axler): https://amzn.to/2T0GpBI
Introduction to Linear Algebra (Strang): https://amzn.to/3dC6kJq
Linear Algebra: Step by Step (Singh): https://amzn.to/2T33G65
3,000 Solved Problems in Linear Algebra (Lipschutz): https://amzn.to/3j2nJMw

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.

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### 43 Responses to “VECTOR SPACES – LINEAR ALGEBRA”

Nice explanation

2. Suong Thol says:

good video thanks

3. Shah Bhuiyan says:

a polynomial with an non-integer exponent is not a polynomial btw

4. Ameena Moos says:

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.

5. Jp says:

good

6. Jp says:

good

7. Jp says:

good

8. Günay Mirzeli says:

I don’t understand nothing ☹️

9. Aramatos says:

isnt deegre zero for polynomials the coefficient a_0 without the t variable? cause degree 1 is a_1*t. I think Axler defines the degree of the vector 0 in this case a negative infinity but I'm not sure. I actually came to this video after reading the sheldon axler book and being confused about polynomial vector spaces.

10. salih şendil says:

You saved my life

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

12. Alex B. says:

helll yeah dub.. thx Big Chrev

13. Anirudh Santhosh says:

You sound like John krasinski!

14. sai chaithrik says:

Thanks you sir you are the best

15. sai chaithrik says:

One of the best explanation ever

16. shrouq makki says:

should we draw?

17. Amanuel Kassa says:

This is a great explanation. Thanks.

18. Amanuel Kassa says:

This is a great explanation. Thanks.

19. Eeby Deeby says:

thank you for good lecture

20. Mr Booshit says:

I am still confused, im still stuck in the physics definition of a vector.

21. Mahima Pareek says:

22. Hyder Focus says:

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?

23. Patricio Dillon says:

Thanks

24. WontonZ Z says:

This is instruction is so much easier to understand comparing to my prof ! ! !

25. Sülgün Rejepova says:

Great explanation Sir big thanks

26. Tarık Arslanoglu says:

What if you scale your p(t) by zero. doesn't that make the degree zero?(for the last statement you proved!)
Thank you for lectures btw.

27. TRIGGER says:

I think you have to mention the >Field< over which you are defining these vector spaces.

28. Mbua Oscar says:

Please I want a tutorial session

@8:58 Degree of a polynomial is always a positive integer, it cannot be in fraction. So that example is not a polynomial.

30. Nathan Holbrook says:

"If you've never looked at a polynomial before."…. c'mon dude. Know your audience.

31. Jaideep Kumar P M says:

Is it necessary that addition is defined for all elements of vector space..or it is enough that the sum of defined elements exist within vector space. Consider Set of all matrixes(including different orders)

32. Edmond Malepane says:

I still don't get it … this is difficult for me

33. Sean Yang says:

Better than my linear algebra prof. VeRy VErY HelPFuL! No reason to go to lectures.

34. Andrew Burnette says:

So far the best explanation on proving vector spaces.

35. Hari Neupane says:

Thank you from nepal

36. Azul Tarmizi says:

could be better if you have a pointer on which part of the slide you're talking

37. Shivam Mandhotra says:

38. A B says:

Great video. Thanks.

39. tae H says:

Thanks

40. Y Zhao says:

If two or three axioms are good enough to proof things, why we need to have ten?

41. Saifullah says:

(Y)