What is a Vector Space? (Abstract Algebra)

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  • Опубликовано: 20 янв 2025

Комментарии • 615

  • @alanveiga452
    @alanveiga452 2 года назад +136

    You explained in 7 minutes what my professor couldn't explain in a whole semester during two hours lectures.

    • @philosophyversuslogic
      @philosophyversuslogic Год назад +8

      But she might be learning it in a way like you did: hearing those boring lectures. Yes, sometimes it is, but by that a lecturer wants you to start doing something by yourself - to put more efforts.

    • @aidanbrown7137
      @aidanbrown7137 11 месяцев назад

      @@philosophyversuslogic Nah. It's just hard to get people who are really good at somethng AND also good at explaining/teaching it, WITH the inuition to understand the pain points from the point of view of the student. Truth is students are given textbooks, boring lectures, teachers who don't have the time or ability to explain things, and no time to properly learn. The vast majority of professors are simply doing a job they must do (ie. get through x amount of material in y amount of time). You are excusing their utter dogshit "teaching" practices. Yes, you absolutely need to learn on your own, but having a bad teacher with poor explanations WAISTING YOUR TIME is FORCING you to learn on your own in a way that is not just unoptmial, but harmful to the student.
      Imagine theres 2 scenarios: #1 Student sits in a 2 hour lecture explaining 10 concepts in which 10% is retained (1 concept), ends up spending the same amount of time if not more trying to understand the remaining 9. The student is confused, and thus must spend an exhuberent amount of time trying to understand. #2 Student sits in a 1 hour lecture in which 2 core concepts are explained WELL, and 8 oncepts are very lightly brushed up on, with recommendations/material offered for the student to study outside of class.

    • @hacrafts2879
      @hacrafts2879 6 месяцев назад

      @@alanveiga452 yes bro

  • @Rainsong777
    @Rainsong777 7 лет назад +353

    Thank you so much for making it easy and simple to understand, and yet not "talking down" to any new students of the subject.

    • @SigSelect
      @SigSelect 5 лет назад +13

      Honestly this channel sets the standard for online education resources.

    • @Grassmpl
      @Grassmpl 3 года назад

      Easy and simple. Ha. Way to repeat yourself.
      I find you funny and hilarious.

    • @Grassmpl
      @Grassmpl 3 года назад

      So easy, y u no da study and no eh prus u failure. Ai yah!

    • @sadiaaa1373
      @sadiaaa1373 3 месяца назад

      @@Grassmpl calm down

  • @rationaloptimist5747
    @rationaloptimist5747 2 года назад +21

    One of the few who don't give a text book definition but actually try to explain the logic behind it.

  • @WithASideOfFries
    @WithASideOfFries 7 лет назад +142

    Simple, poignant, and well-executed. This is an underrated channel that can easily make advanced mathematics accessible.

    • @Socratica
      @Socratica  7 лет назад +41

      You are so kind, thank you.
      This is truly our goal - we love math, and we think everyone deserves the chance to learn.
      We would really appreciate it if you would share our videos with your friends - on Twitter, Reddit, etc.
      That will really help us grow!
      Thanks again for watching and for leaving such an encouraging comment. It really makes us excited to make more videos! :)

    • @wajidhussain7040
      @wajidhussain7040 4 года назад

      @@Socratica appreciable

    • @Grassmpl
      @Grassmpl 3 года назад

      @@Socratica how about some content on homology groups? Eg. Mayer Viertoris sequence etc. I find that stuff difficult to understand.

  • @Songvbm
    @Songvbm 5 лет назад +60

    I swear to god, I am in love with this channel. Linear Algebra is NOW MADE EASY.

  • @joshsmit779
    @joshsmit779 8 лет назад +367

    I like that socratica chooses to cover abstract subjects.

    • @pokertable
      @pokertable 8 лет назад +2

      indeed!!

    • @okoyoso
      @okoyoso 5 лет назад +7

      @eh6794 Vector spaces and modules in pre-calc?

    • @Moreoverover
      @Moreoverover 4 года назад +3

      @eh6794 Pre calculus lol, in what university?

    • @Moreoverover
      @Moreoverover 4 года назад

      @Artificial Resonance How old were you? Was it a private school?

    • @vainbow4632
      @vainbow4632 3 года назад +4

      @Artificial Resonance No you didn't lol, this is not part of any European high school curriculum. You probably learned about vectors and operations on vectors, and can't tell those apart from the algebraic structure that is a vector space.

  • @danielsmirnov6736
    @danielsmirnov6736 2 года назад +9

    Arguably the best and simplest explanation of a vector space I've ever heard. Thanks a bunch!

  • @SkippyDoPe
    @SkippyDoPe Год назад +5

    Took a "complex" thing and made it simple and clear, thank you

  • @ARCT3CH
    @ARCT3CH 8 лет назад +64

    Thank yooooo!!!! I'm taking linear algebra with a midterm test in 2 days. The book throws all these rules about vector spaces but never does it take the time to explain or help visualize WHAT a vector space actually represents. I can memorize the rules but I just felt so lost.... But this really helped me.

    • @Socratica
      @Socratica  8 лет назад +22

      We're so glad to hear this helped! Visualizing math/physics is one of the best uses of video, we think - it really adds something to your textbook reading that's hard to do just in your head!
      Good luck on your midterm!! :)

  • @user-ih7iq6bw5o
    @user-ih7iq6bw5o 2 года назад +9

    I can't thank you enough for this. Your amazing videos make my university lectures so, so much easier to digest.

  • @arya8192
    @arya8192 3 года назад +5

    You are the maths teacher I have been looking for. Thank you so much socratica for helping many of us to imagine the concepts from maths.

  • @loden5677
    @loden5677 2 года назад +1

    This series on abstract algebra is the best thing I’ve ever seen

    • @Socratica
      @Socratica  2 года назад +1

      You're so kind, thank you for this encouraging message! 💜🦉

    • @loden5677
      @loden5677 2 года назад

      @@Socratica Thank you! I wish you had a Linear Algebra series too!

  • @infinitymfg5397
    @infinitymfg5397 7 лет назад +57

    I love this channel. I went back and looked at some of the earliest videos and the progress is amazing. You've come a long way from a 1 minute video on a powerpoint slide. This is one of my favorite channels when I need something complicated explained.

    • @Socratica
      @Socratica  7 лет назад +16

      That is so kind of you to say, thank you!! It has truly been a labour of love. We are completely self-taught filmmakers and editors, and it's been a real education! :)

  • @kaycee5747
    @kaycee5747 6 лет назад +3

    I have an exam in three days, and you just helped me understand vector space better than my teacher and textbook. I feel more comfortable with the topic and have a better grasp of it. Thank you!

  • @kellymoses8566
    @kellymoses8566 3 месяца назад +3

    I'm reading a paper that uses vectors and matrix multiplication to determine what routers can reach each other. Linear algebra is insanely versatile.

  • @bandlelihlemncube5448
    @bandlelihlemncube5448 3 года назад +3

    fluent to the point and distinctively i like it

  • @pinedelgado4743
    @pinedelgado4743 3 года назад +14

    This is awesome stuff, Socratica!!! It's very, very easy to become a huge fan of abstract algebra watching videos like these!!! :) :)

  • @abdeldjalilselama2490
    @abdeldjalilselama2490 4 года назад +4

    I'm New here and as an Electrical & Electronic engineer student i like your way of explaining thing , work hard for more great content ( you already earned my subscription)

  • @guitarttimman
    @guitarttimman 4 года назад +2

    Theoretical Physics only goes so far, but theoretical mathematics has no boundaries. As physicists climb the prongs of theory, we will start needing more tools to utilize for the purpose of measurement and evaluation. You're awesome! Thank you.

  • @elizabethreyna8354
    @elizabethreyna8354 2 года назад

    This is the best explanaition ever. This video most be the first one. No other one explains much better than this. New sub

  • @atashaker
    @atashaker 5 лет назад +3

    I understood a 2-hour course in less than ten minutes. Thanks

  • @gloriouswingsresearch4206
    @gloriouswingsresearch4206 7 лет назад +1

    I JUST BEGAN TO FALL IN LOVE AGAIN WITH ALGEBRA. IT LIKE SHOWING ME SOME SCIENCE OF QUANTITIES IN THE UNDERGROUND. SO SWEET.

  • @adithyaparupudi1336
    @adithyaparupudi1336 4 года назад +4

    woow. I am so lucky to have found this channel. Its like a gold mine here.. such awesome explanation! And highly immersive for a dry topic when studied from text books!

    • @Socratica
      @Socratica  4 года назад

      We're so glad you've found us!! 💜🦉

  • @struggler_ladka
    @struggler_ladka 3 месяца назад

    Only channel on youtube that really explain the login behind the definitions 👍

  • @HarpreetSingh-ke2zk
    @HarpreetSingh-ke2zk 2 года назад

    In addition to a beautiful presentation, the presenters carefully select their attire and background.
    To me, this is extremely calming to the eyes and facilitates the brain's storage of the concept.

  • @goverdhanc2930
    @goverdhanc2930 7 лет назад +1

    It has become my favourite channel. Concepts are nicely explained.

  • @cybersecuritydivisionmanga955
    @cybersecuritydivisionmanga955 Год назад

    By far the bestestestest of all the abstract algebra lectures in this world..

  • @mukulverma9375
    @mukulverma9375 2 года назад +3

    I'm speechless. Such a clear and precise explanation, really makes me happy that I stumbled upon your channel! Big thanks from a student who was facing a hard time understanding these abstract concepts. I'm going to watch all the videos related to my syllabus, that has been covered by you guys. Peace!

  • @jakewilliams9802
    @jakewilliams9802 7 лет назад +5

    This is an incredibly helpful video, I was unsure of what a vector space actually was but this video explained it ridiculously well. Thank you.

  • @ShubhamSharma-hx4df
    @ShubhamSharma-hx4df 3 года назад +2

    This channel has got a new subscriber today.
    Just amazing explanation. Keep making such useful videos

  • @karllaurenzdiamante3784
    @karllaurenzdiamante3784 4 года назад +1

    This channel is a hidden gem. Thank you so much.

  • @susantabasu9570
    @susantabasu9570 3 года назад

    Thank you sosoooo much. This is an underrated channel.

  • @TheBirdMan
    @TheBirdMan 7 лет назад +1

    I would have to say that finally I understood what is a vector space. I wish someone would have taught me like this. Needless to say I scored a B+ on Linear Algebra and don't know what is a vector space ! You are great ! Keep up the good work !

    • @Grassmpl
      @Grassmpl 3 года назад

      A B+ in math? Ooh I hope you don't have Asian parents

  • @Socratica
    @Socratica  3 года назад +8

    Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra

    • @Grassmpl
      @Grassmpl 3 года назад +3

      The "ow" and the pointing vectors were so cute. Makes me wanna hug this lady.

    • @egl3
      @egl3 3 года назад

      How to get blue shirt like you

  • @claudefazio
    @claudefazio 3 года назад

    This might just be the best RUclips channel on mathematics! Great lectures!

  • @plaidklaus3407
    @plaidklaus3407 4 года назад

    This is an excellent demonstration of teaching at a comfortable rate with succinct information that is easily digestible.

  • @slannastro2023
    @slannastro2023 2 года назад

    Before taking first upper div (linear algebra) course, this is video is strongly recommended. I believe most instructors can't teach as clear as this lady.

  • @cristian-bull
    @cristian-bull 6 лет назад +335

    A physicist and a mathematician are in a congress and the talk goes like:
    "If we consider an 8 dimensional sphere, we can show that the radio..."
    The physicist, skeptical, ask the mathematician:
    - "Do you believe such nonsense about 8 dimensional spaces?"
    - "Sure, of course"
    - "So.. how do you "see" an 8 dimensional sphere?"
    - "Easy. I imagine a N dimensional sphere, and then set N equals 8".

    • @tauhid9983
      @tauhid9983 5 лет назад +55

      While a theoretical physicist is simply enjoying the debate

    • @goyonman9655
      @goyonman9655 5 лет назад +53

      An engineer looks at them as looney

    • @tauhid9983
      @tauhid9983 5 лет назад +11

      @@goyonman9655 Theoretical physicist leaves the chat for PEACE!

    • @lauterunvollkommenheit4344
      @lauterunvollkommenheit4344 5 лет назад +12

      In my experience, physicists know the difference between mathematical space and physical space.

    • @tauhid9983
      @tauhid9983 5 лет назад +2

      @@lauterunvollkommenheit4344 wrong.... "physicists" is a very general term... when u say "physicsit" do u mean experimental, theoretical, mathematical...depending on which physicsit u are, u'll understand and interpret math stuff differently. Cheers!

  • @philosophyversuslogic
    @philosophyversuslogic Год назад +3

    This teacher is ideal. The lessons are not only informative, and highly intellectual, they are lovely!

  • @chandrasekarnarayan8233
    @chandrasekarnarayan8233 6 лет назад +22

    Vectors addition, multiplication rules can be a applied to n-dimensions. In Computer Games like Age of Empires 5 dimensions are Food, Wood, Gold, Stone, Population.

    • @Socratica
      @Socratica  6 лет назад +8

      AoE is the bestest of the best. Thanks for making this interesting connection.

    • @waheedullahhameed8354
      @waheedullahhameed8354 5 лет назад

      You mean Age of Empires ll, right!

    • @tomctutor
      @tomctutor 3 года назад

      More abstractly I tell my students that a vector is just an ordered set of elements
      {a,b,c}={b,a,c} is a set but (a,b,c) =/= (b,a,c) is a vector.

  • @mathstoinfinityclassinTamizhla
    @mathstoinfinityclassinTamizhla 5 лет назад +1

    I love your teaching 😍 it is not easy to focus on studies when you have financial crisis .I can focus on the study without distraction in your RUclips channel. Thanks

  • @learnerlearns
    @learnerlearns 8 лет назад +1

    Superb concise lucid presentation! Good writing, splendid narration, + graphics and simple practical examples make this easy to follow.

  • @vladimirkolovrat2846
    @vladimirkolovrat2846 4 года назад

    I love your channel. Your presentation is clear and creative and polished. I often learn new things here, and sometimes I understand things I was "taught" in the past, for the first time.

  • @applelover27
    @applelover27 7 лет назад

    This is by far the best explanation ive seen on this topic

  • @heidarsafari4753
    @heidarsafari4753 2 года назад

    Thank you so much for making the concept of vector space and vector definition extension explicit with your perfect teaching.
    🌹🌹🌹

  • @DNJ9o9o
    @DNJ9o9o 4 года назад

    Rarely do I subscribe to a channel just by watching one video, but this time I did. Thanks for the high quality video!

  • @manisharya3744
    @manisharya3744 6 лет назад

    Style of explanation is awesome. I like the way you touched the arrow at the end.

  • @solvicode
    @solvicode 7 лет назад +6

    You just saved me hours of research!

  • @harishdhyani7810
    @harishdhyani7810 5 лет назад +1

    Excellent explanation in a short video. Bravo

  • @thesexrace
    @thesexrace Месяц назад +1

    Thank you for this video! 😀

  • @mohabsoliman7172
    @mohabsoliman7172 5 лет назад +1

    i've taken vector spaces 2 years ago and finlay i understand it this day. thank you so much

    • @Grassmpl
      @Grassmpl 3 года назад

      I understood them right from the beginning in lecture. They are not that difficult.

  • @NextGenAge
    @NextGenAge 2 года назад

    First video I watch, you got yourself a new subscriber!

  • @DiegoAndrade
    @DiegoAndrade 8 лет назад +75

    Can you make a video on tensor and tensor fields?

    • @ferencrarosi8101
      @ferencrarosi8101 5 лет назад +2

      Would be tougher... :)

    • @MTB_Nephi
      @MTB_Nephi 5 лет назад +2

      Yes, please !!
      @diego andrade or you choose " Tensor for beginners "

    • @hank1519
      @hank1519 5 лет назад +1

      @@MTB_Nephi or for the hopelessly discouraged student.

    • @Grassmpl
      @Grassmpl 3 года назад

      Not to be confused with tensor products.

  • @m.a497
    @m.a497 4 года назад

    I watched many videos on vector space but i did not understand... But ma'am you explained very well and in better way. Thanks

  • @animeshsinghal3405
    @animeshsinghal3405 3 года назад

    Very engaging teaching and presentation style. Have finally grasped the concept. Thanks :)

  • @RitamPramanikmusic
    @RitamPramanikmusic 4 года назад

    It was so clear and interactive...I am a Masters students and I was trying to understand this topic from a so so boring lecture of a professor.....Thanks to this team atlast I could get on it :)

    • @Grassmpl
      @Grassmpl 3 года назад

      What do you study? You're a masters student but can't understand an undergraduate level concept?

  • @danzap3844
    @danzap3844 3 года назад

    Dankeschön für die Auffrischung. Sehr verständlich erklärt.

  • @akhtaralikhan9096
    @akhtaralikhan9096 4 года назад

    1hour College class = 6 minute video fantastic Job thaNks Socratica for that effort

  • @stevenlin6106
    @stevenlin6106 2 года назад

    Great effort! I really enjoyed your videos as I am trying to teach my son math in the middle school.

  • @LizardBoy2211
    @LizardBoy2211 6 лет назад +1

    The sound effects make it sound so sci-fi. Awesome.

  • @richaagarwal9727
    @richaagarwal9727 5 лет назад

    Awesome video! also left a smile on my face at the end...U r really helping students explaining stuff books don't (even my prof didn't explain it this way)

  • @miketurner3461
    @miketurner3461 5 лет назад

    Socratica has some of the clearest explanation out there

  • @gaming_boga
    @gaming_boga 5 лет назад

    hi socratica ur explanation way is really very good . Hope that some day our teachers will also learn this kind of way of teaching

  • @JimSmith-u5g
    @JimSmith-u5g Год назад +2

    Is zero vector a starting point? It’s been a wonderful teaching that you give thank you for creating this

  • @ramankaushish7720
    @ramankaushish7720 2 года назад

    beautiful channel and explanation of concepts... regretting to discover it so late..still very helpful

    • @Socratica
      @Socratica  2 года назад +1

      We're so glad you finally found us!! 💜🦉

    • @ramankaushish7720
      @ramankaushish7720 2 года назад

      @@Socratica its a win win for me.. 💕

  • @wilbert_delarosa
    @wilbert_delarosa 4 года назад +1

    That was a really good explanation

  • @astraguardian
    @astraguardian 7 лет назад

    you guys are amazing... truly.... I am so thankful for these videos. Please keep this channel up and make more videos. Thanks alot

  • @gisellelong7016
    @gisellelong7016 5 лет назад

    your lectures are awesome! So much better than my lectures at school

  • @TheTuntunpa
    @TheTuntunpa 8 лет назад +1

    Never stop making this videos! Oh my GAWD i love them so much!

  • @noorhassanwazir8133
    @noorhassanwazir8133 4 года назад

    Nice madam prepare more lectures so that people get more benefits and knowledge from ur skill,experience and knowledge.ur way of teaching is outstanding

  • @taraspokalchuk7256
    @taraspokalchuk7256 8 лет назад +6

    after al this definitions it would be nice to see their applications to proofs

  • @Rgrazia1
    @Rgrazia1 7 лет назад

    This is the best presentation there is.

  • @joydebroy8
    @joydebroy8 3 года назад +1

    Explained very well....Thank you.

  • @amberimtiaz1677
    @amberimtiaz1677 4 года назад

    Just amazing...... got idea of vector space ......... very broadly the topic is explained ,at the beginning I was thinking vector space are just vectors .......thank you.......

  • @kashishmittal9516
    @kashishmittal9516 2 года назад +1

    It's just really damn awesome. I learned vector spaces in a way that i could never have imagined. Really impressive 😍. Thank you ❤️

  • @user-jm7bo1ek4r
    @user-jm7bo1ek4r 7 лет назад +2

    honestly love your channel! it helped me understand this thank you !! just subscribed

    • @Socratica
      @Socratica  7 лет назад

      We're so glad to hear this! Thanks so much for subscribing - we're so happy you're watching! :)

  • @newelixir1018
    @newelixir1018 5 лет назад

    Most awesome teacher of higher mathematics...thank you for making maths easier for us...

  • @JorgeGomez-li9td
    @JorgeGomez-li9td 8 лет назад

    This videos are the best, the las year i saw a course of Groups and Rings, and was nice watch this videos and remenber those classes, thanks for the amaizing work in this videos i am waiting for more, a big hug from Colombia!

  • @hopscotch35
    @hopscotch35 5 лет назад +1

    Love this channel - wish I had encountered these subjects at school

  • @arslanmehar5931
    @arslanmehar5931 4 года назад

    Well done i am always confused in the vector space you explain it very well

  • @zippydipity42
    @zippydipity42 8 лет назад +4

    This video was soo much more useful than Khan's! Well done!

  • @Kanpurwale2244
    @Kanpurwale2244 3 года назад

    One of the best teacher.

  • @kofY84
    @kofY84 3 года назад

    I need to comment just because the ending, that was pretty cool :)

  • @onyangosylvester6353
    @onyangosylvester6353 6 лет назад

    This is spectacular.... You've actually explained it very well and I like it

  • @satiwandass145
    @satiwandass145 6 лет назад

    The way to explain things very easy and simple,which I like it. thanks

  • @ali_ahmed31899
    @ali_ahmed31899 5 лет назад +1

    Thank you so much you help me to understand linear Algebra you are brilliant God bless you

  • @benzeltser9851
    @benzeltser9851 3 года назад +1

    AMAZING JOB

  • @resistencialiberal9555
    @resistencialiberal9555 2 года назад +1

    My prof sounds like he smokes crack before every single lecture. It is a nightmare. Thanks for a comprehensive video.

  • @shivansh_gupta02
    @shivansh_gupta02 3 года назад

    The idea of pointy vectors is awesome.

  • @mlazos
    @mlazos 8 лет назад +2

    Good job.
    Really nice quality videos.

  • @vanguard7674
    @vanguard7674 8 лет назад +25

    Keep it up I love this. Do Galois Theory next :DD

  • @Alkis05
    @Alkis05 4 года назад

    One of the most amazing example of vector spaces is the one that embeds words (that is, a function that turns a word to a n-D vector). When you embed words as multi-dimentional vectors in such a way that vectors that are close together (that is, vectors that have similar norm and close to "angle" are close to 0º) means that they have semantic proximity you get to do vector arithmetics with words.
    That is, if you start if vector for "king", subtract "man" and add "woman", the result is vector that will be pretty close to vectors corresponding to "queen, princess, etc.."
    These vector spaces dimensions often hit the mark of hundreds.

  • @haroonrasheed1144
    @haroonrasheed1144 7 лет назад

    Amazing.Do more videoes.You are very good at explaining the things.

  • @richardd7614
    @richardd7614 2 года назад +5

    study math they said, no harm can come to you they said - lecturer immediately gets attacked by vectors. I'm done back to shop class where it's safe.

  • @nouriaaouail9643
    @nouriaaouail9643 11 месяцев назад

    really a great and very clear explanation, thanks

  • @chessmanwriter12
    @chessmanwriter12 6 лет назад

    Very nice and easy to understand explanations!

  • @ciprianandrei5751
    @ciprianandrei5751 8 лет назад +2

    very well explained, great video! keep going on

  • @prvns8586
    @prvns8586 8 лет назад +2

    too simple to understand
    the best video I found for vector space..!!!

  • @deepikakumari2749
    @deepikakumari2749 6 лет назад

    Your explanation is great...I like your channel..it helps a lot in studying algebra..pls make more videos on modern algebra and other math topics also.

  • @vinayganagalla2404
    @vinayganagalla2404 8 месяцев назад

    Thank you for sharing like 7 years back! its very helpful now and relevant to AI space.