What is...a quotient vector space?
Вставка
- Опубліковано 13 бер 2021
- Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...a quotient vector space? Or: Identifying information.
Slides.
www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Nicely done! Your “clickbait” title slide 😉 “Parallel lines are points?” zeroed in on one of the intuitively difficult aspects, at least for me, of the quotient vector space concept. I’ve read and heard many lecturers talk about “zeroing out” the vector subspace but none actually explained and demonstrated it nearly as well. The typical textbook approach of introducing the formal definitions then jumping through theorems wasn’t working for me - I kept getting stuck on “but what is going on?” Your excellent graphics and examples filled in the missing intuition that then let me grasp the more formal framework. Your analogies with information and group theory also helped me to get to “oh, I get it now”. Thanks and I’ll be investing my time to check out your library of material as I explore more topics!
Hah, clickbait - the essence of UA-cam ;-) And it worked!
Just kidding of course: I am glad that the video was helpful!
I can feel you by the way: it took me many attempts to understand the textbooks, and I still do not claim that I am there... It is a bit of a strange culture that written math is so different from "real" math.
Anyway, I hope that my attempt of explaining quotient spaces works for you and others as well. It worked for me, so I hope others feel the same! Of course, I got it from somewhere else - I do not own the copyrights ;-) Standing on the shoulders of giants!
Sir, I was struggling so hard in my linear algebra classes and your videos saved my life from the upcoming tests.
Thank you so much for posting this content!
Thank you for the feedback. It is always good to hear that the videos are helpful.
Tests are usually "random noise", so everyone needs luck, i.e.: Good luck with your tests!
P.S.: Please drop the “Sir” ;-) We are all humans, so we are all equals.
amazing concise useful video ! I really like the concept of ‘collapsing’ a vector space onto W - its brilliant to visualise what’s actually happening
Thank you so much; I am glad that you liked the video 😁
I hope you will enjoy your linear algebra journey 👍
Excellent! Btw is there any author out there who wrote/writes book the way you explain? Overview+intuition described informally then the rigorous treatment.... Let me know plz.
Thanks for the feedback; glad that you liked the video and I hope it was helpful.
Regarding your question:
- The good news is that there are plenty of books following the same strategy - mixing intuition and rigorous treatment.
- The bad news is that this is not so easy to nail down onto an author since most authors write never more than one book.
In general, newer books have a bigger chance to be written with intuition in the focus since the writing style in math is very much changing over time but constant for about 2 decades.
For linear algebra I enjoyed reading (your taste might be different, of course!):
- Strang’s “Linear algebra and its applications”. The main upshot are that it is “not short on details and explanations at the same time, and, even better, there is a video series: ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/
- Axler’s “Linear algebra done right” (often recommended as a second but not first reading; I kind of agree but I enjoyed it as a first reading); and its free: web.math.ucsb.edu/~agboola/teaching/2021/spring/108A/axler.pdf
- Tao is great and free (and the same as for Axler applies): www.math.ucla.edu/~tao/resource/general/115a.3.02f/
- Also try this side: math.stackexchange.com/questions/4335/where-to-start-learning-linear-algebra
If you have another topic in mind, let me know and I can make a recommendation as well.
I hope that helps!
Thank you so much! This was really helpful
Welcome! The quotient vector space is a bit mysterious on first sight, and I hope the more intuitive explanation helped!
Great video thanks
Thanks for watching, you are very welcome! I hope you will enjoy linear algebra.
Great video! Thank you! "The usual yoga 😂"
The usual Yoga: you are welcome 😁
Seriously, you are very welcome.
Wow, W could be kid or adult in V person, and then all kids in V / W are equal...
Yes, we are all equal - I like that ;-)