We introduce vector spaces in linear algebra.

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Linear Algebra:

*–Recommended Textbooks–*
Linear Algebra and Its Applications (Lay):
Linear Algebra Done Right (Axler):
Introduction to Linear Algebra (Strang):
Linear Algebra: Step by Step (Singh):
3,000 Solved Problems in Linear Algebra (Lipschutz):

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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  1. Kasa Madhu says:

    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:


  6. Jp says:


  7. Jp says:


  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

  11. Syad says:

    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:

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

  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:


  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

  29. Shrey Wadhwa says:

    @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:

    Very helpful

  38. A B says:

    Great video. Thanks.

  39. tae H says:


  40. Y Zhao says:

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

  41. Saifullah says:


  42. simonel garrad says:

    At 6:27,what were you saying 1 to the right 2 up and 3 to the left and 1 down? what does this mean?

  43. Abubakar Seyruu says:

    very satisfied lessons

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