Linear subspaces | Vectors and spaces | Linear Algebra

No video

Linear subspaces | Vectors and spaces | Linear Algebra | Khan Academy

Рет қаралды 1,547,404

Күн бұрын

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/line...
Introduction to linear subspaces of Rn
Watch the next lesson: www.khanacademy.org/math/line...
Missed the previous lesson?
www.khanacademy.org/math/line...
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: / channel
Subscribe to KhanAcademy: kzfaq.info_...

Пікірлер: 298

@tauceti8341 9 жыл бұрын

+ V is a subspace (0-6:00) - V contains the 0 vector: (2:26-2:44) - Closed under multiplication: (2:47-4:23) - Closed under addition : (4:28-5:35) Subspace 3 points ; subspace & closure under (A & M) Examples using concepts: proving a subset (S) is/not a subspace - (08:55-14:17) Span (v1, v2, v3) is a valid subspace of R^n? - (14:21-19:42) Visualizing if a simple vector can be a subpsace. U = span([1, 1]) (19:43)

@blakiwhite5664 8 жыл бұрын

+Tau Ceti The world needs more people like u

@txuezea4072 2 жыл бұрын

Thanks

@AdhikariMohan 11 жыл бұрын

Amazing..I spent past 7 hours trying to understand subspaces from my notes with no success and now its crystal clear in just 23.5 minutes. A huge THANKS to You!!

@yangvely7018 7 жыл бұрын

You are better than my professor lol. I dont know why I attend college.....

@7thFormVoid 5 жыл бұрын

So you can get a real degree?

@That_One_Guy... 5 жыл бұрын

Yeah, to get degree so you can get a job, that's so annoying

@Nomnomnom165 4 жыл бұрын

@@That_One_Guy... I'm in college and the companies I'm aiming for don't need degrees. They're just insanely hard for everyone to get into

@codingtheworld674 4 жыл бұрын

If you are just learning mathematics in your college, so you don't need to go. We should not be in college just for a degree paper, do more things(-like starting a new projects,etc.)...

@daehwankim4246 4 жыл бұрын

ㅇㅇ

@ypenburger 11 жыл бұрын

me looking in my linear algebra book: dafuq??? me looking in the same book after a video from khanacademy: Aha!

@roxyfrank5679 3 жыл бұрын

facts

@Con2tnaep 3 жыл бұрын

init fact

@heacac3729 20 күн бұрын

factos

@VineetontheBeat 12 жыл бұрын

This is so good. Teachers usually go straight into complex examples and totally roll over the concepts. You make the concepts clear and concise. Thanks so much!

@TheBananahulk 8 жыл бұрын

Haha if you look at the statistics. The viewer count always goes up before exam periods :P

@laartisticfellow2382 5 жыл бұрын

Im a student of statistics and i can vouch for that

@Iluminent 5 жыл бұрын

crazy thought you got there, I wonder why that is...

@Xxjorgex123 4 жыл бұрын

how you figured that out genius?

@Shy_Guy11 11 жыл бұрын

In addition to that, he is great at explaining all these concepts to people who have little or no idea about the subject. Most people don't realize this, but this is extremely difficult to do for most people, but he is able to get into the mindset of a person who is new to this stuff, and explain it in such a way despite his great understanding of the subject. Thank you Sal for all your hard work..

@rahulkiroriwal8779 3 жыл бұрын

hello there , how are u . its been 8 years

@romeo5239 5 ай бұрын

@@rahulkiroriwal8779 now 11

@dalisabe62 Жыл бұрын

I love his style and voice. His detailed persistent explanations show how much he is capable of relating to his audience and how much experience he has in teaching. I found him the best explainer that is out there for concepts that are typically confusing or need further breakdown.

@bryancolon5090 3 жыл бұрын

Thank you so much. When you stated between 5:10-5:30 that we're simply choosing vectors within the given parameters of our space V and then adding them together to see if the resultant vector was still in space V, everything finally clicked. I immediately understood what "closed under addition" and "closed under scalar multiplication" meant. Words cannot describe my gratitude! Thank you!

@neomarc9946 7 жыл бұрын

Thank you sir for making it 100% easier. My professor sucks af.

@Sundoren 9 жыл бұрын

superb voice superb explanation superb colors why we dont have teachers like u damn

@Hepichack 9 жыл бұрын

Congratulations man !!! They way you teach is very clear-easy-good,not only because you explain them with great way,but because you used examples,and you used Cartesian plane to show how vectors works in reality. That really helps,because to understand something in maths,you need to implement it. Keep the good job !!!

@Hemenmyname 10 жыл бұрын

I personally am thankful for your service sir, thank you very much.

@lolalukie713 11 жыл бұрын

you accomplished in 23 mins what my linear algebra prof couldn't in two 2 hour lectures.

@rahulkiroriwal8779 3 жыл бұрын

hey how u doing , its been 8 years ?

@lolalukie713 3 жыл бұрын

@@rahulkiroriwal8779 I have my degree in Mechanical Engineering and am working as a project engineer for construction projects and have started a business on the side ! Thanks for checking :D

@bookman9897 2 жыл бұрын

@@lolalukie713 wow really great keep growing

@devilpizza123 13 жыл бұрын

thanks! my lecturer is terrible at explaining this stuff and uses all the extremely abstract notation stuff that no body understands. your explanations are easy to understand and make difficult to grasp concepts simple. i love it!

@cwruhsk5 13 жыл бұрын

Wow..... I spent five hours trying to learn this, and still could not comprehend the material. 20 minutes of this video, and everything makes sense now. This is awesome!!!

@EchoL0C0 11 жыл бұрын

Thank you so much for taking the time to make this video! I really appreciate the fact that you take the effort to try to connect these concepts in many different ways, like in terms of things we've already learned, or what works and what doesn't, instead of just the formal mathematical definition. I mean, appreciate the formal mathematical definition, (I like math because it seeks "truth without error") but it's not much use if I don't understand things in the first place. Anyway, thanks!

@snake10566 11 жыл бұрын

The way you define everything in simplistic terms is amazing. Thank you so much.

@rapid1010 5 жыл бұрын

You're presentations are very clear and you're a great teacher as well.Thank you very much for these videos!

@LAnonHubbard 13 жыл бұрын

Very cool explanation. I've been trying to teach myself this sort of stuff from books and Wikipedia. They're too dry for my current level of knowledge. Your dynamic presentation is exactly what I need and I'm sure will help me to understand other resources.

@sauryashrestha 8 жыл бұрын

I highly recommend this video. The presence of a graph makes it much easier to comprehend!

@0dablkin0 11 жыл бұрын

Thank you very much, my professor is blowing through this information leaving me wondering what just happened, you are helping me keep pace with the lessons

@ocsantiago 14 жыл бұрын

This is great. I just discovered your library as well. Great stuff!!

@hellokat68 10 жыл бұрын

thanks so much, you help me learn all these math concepts that I were unable to grasp in class when I was in school

@makavelic2000 11 жыл бұрын

I LOVE YOU. This helped so much. was freaking out about this class and was about to drop it, but now i understand enough to not panic.

@nturner4 13 жыл бұрын

wow this is awesome. this is SO much more helpful than any lecture I've been to this year!

@fukgovernment 10 жыл бұрын

You deserve a noble price. Thanks

@anonymoose8829 10 жыл бұрын

Nobel Prize? :P

@inteusproductions 9 жыл бұрын

Nolen Lah Nope, just a noble one

@Sundoren 9 жыл бұрын

inteusproductions :DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

@StephenRayner 9 жыл бұрын

inteusproductions Haha, he sure does, but none are given for teaching.

@enjoyablesounds 14 жыл бұрын

Thank you sal, you are a great example of a good human being. With all negativity around the world you give me hope. Thank you so so much :)

@fuckooo 11 жыл бұрын

Khan, your linear algebra playlist is a work of art!

@fuzzybuns1234 10 жыл бұрын

Hey Sal, I looooove your videos, first of all. After taking Algebra 1 I told myself I would spend one summer learning all through Calc 1, and, thanks to you, this summer I am attending SacState as a Freshman in high school. I know that this topic is unrelated to the video and that you probably won't even have time to read this, but I was wondering if you have any intuition that you could teach me regarding visualization of Lie groups and symmetries because it's really difficult for me to imagine. I understand how group theory works, but imagining these things as circles and large manifolds is a giant leap from just sets of numbers. Thanks a ton for your videos; I don't know what I would have done without you.

@awesomecodeyay8382 2 жыл бұрын

Nice, I did calc 3 and Diff Eq in 8th grade. I also attended USAMO. Are you a full time student at the university, or are you just taking some courses there? I don't think you can graduate high school right in just one summer. Also, I'd imagine that there are gaps in your mathematical knowledge because you haven't done enough geometry, and you did not spend enough time on the prerequisites of calc. Additionally, doing higher math does not mean a lot. I did Calc BC in school as a 7th grader, and I don't consider my 7th grade self all that smart. Doing calc does not require as much creative thinking as math competitions. Try the first competition to the IMO, which is the AMC 10/12. Try some problems there and see how you do. This competition will probably be hard for someone without much experience. Next, there will be the AIME, which is much much harder. If you want to be better at math, I suggest participating in these competitions.

@fuahuahuatime5196 11 жыл бұрын

Wow, thank you SOO much! My teacher did a HORRIBLE job explaining this. I've tried searching everywhere on youtube... Thanks man! Seeing it visually helps a lot more than just seeing the theorems or whatever proven with random variables with no significance.

@alejandromunoz8086 6 жыл бұрын

You explained to me in under half an hour wait University professor can't explain in 3 lectures. Thank you so much, I understood a hole section in this video

@IndulgeObscenity 14 жыл бұрын

You are truly a great teacher! Than you for the posting!

@SoloPro 8 жыл бұрын

Seriously this explanation was good im so happy i typed it in youtube... defo liked and subbed

@deathmachine91 10 жыл бұрын

You are a better teacher than my professor. Thanks for putting the video up

@phalgunvedantam1388 6 жыл бұрын

Thanks to sal i now understand everything about basis, vector spaces and every other thing right before my tomorrow's exam... Thanks sal

@sarveshc2985 Жыл бұрын

wow what an amazing explanation! I spent too much time looking in notes and couldn't get much out of it

@darrowshire11 12 жыл бұрын

Perfect! Just what i needed! Thx alot

@MrSauce714 13 жыл бұрын

Linear algebra test tomorrow not worried about this topic thanks to you!!!! Great vid!!

@Adam-gp3ij 5 жыл бұрын

That’s pretty clear! Thank you

@timgoppelsroeder121 5 жыл бұрын

Thank you for these tutorials. They are very compact

@homestar92 12 жыл бұрын

These videos are teaching me more than my professor does. You may be saving my grade.

@chvere123 13 жыл бұрын

it really saved me time for understanding these materials, thanks a lot.

@danielgonzalezisaiev9643 11 жыл бұрын

I'm learning crazy much! You already feel like my best friend dear khan academy mystery man.

@beanfant_jesus 4 жыл бұрын

You taught me in 25 minutes what my professor took 2 hours to cover in class. Thank you!

@codingtheworld674 4 жыл бұрын

it is not the first time you have been facing like that a new subject, so that you understood in 25 min.

@A-003 14 жыл бұрын

Thanks you VERY MUCH for the nice, simple, useful explanation. God bless you

@rochelletarin6422 3 жыл бұрын

Well, this made more sense than my teachers lecture. Thank you!

@AvengedRocker92 12 жыл бұрын

Really helped out, thanx for the video!

@preciousgeofrey6192 Жыл бұрын

More gratitudes should be granted to you Sir

@Msmotionocean 9 жыл бұрын

Thanks! This is amazing!

@user-wj5hl7vj8s 9 ай бұрын

You are a life saver, thank you! I fully understand it now.

@SciFiGirl1023 14 жыл бұрын

this helped so much thank you soo much!

@Andradam33 13 жыл бұрын

Making up where my prof lacks - every time. Thanks for your useful explanations and videos.

@Ennendra 11 жыл бұрын

Bro, I know that feel. But this, this is definitely a lifesaver right now :D

@DFsdf3443d 6 жыл бұрын

would it then be correct to say that: Any linear combinations of vectors in a subspace must be equal to a vector that is also in the subspace ? kind of like the closure under addition? just with linear combinations?

@DEEPAKSINGHcreative 4 жыл бұрын

In summary, In order to define subspace using vector we need to define for R^n i.e. for all real value, exculding a certain ranges would bring up the possibilty of subset instead of subspace, SPAN by default are defined for R, hence they automatically fall into subspace cateogory. If there is any example that doesn't include R i.e real domain, please do provide. I think one you have mentioned would be n dimension zero vector, the addition or linear combination again results in zero vector, which is exception of trend, but for non-zero n-dimensional vector space to be termed as subspace, it needs to be defined for 'R' . Note: Here R represents real domain.

@fathimahida8878 6 жыл бұрын

it really helped me... thanku soo much...keep uploading more vedios...

@cnjaify 11 жыл бұрын

thank you sir. u should receive like a humanitarian award for the number of times u have saved my life lol

@eshaghazali2482 4 жыл бұрын

I have a quiz tomorrow God bless you sal!! 😭

@aandha1 13 жыл бұрын

This guy is just unbelievale !! Thumbs upp!!!

@user-vv4fg6pi9n 3 жыл бұрын

this was such a great review before my first test

@stephaniepaul2010 11 жыл бұрын

crazy to think i'm paying £9k a year tuition fees, but learn the course from these videos! Thankyou! :)

@teddybeitler 14 жыл бұрын

once again, you have saved me. thank you sir!

@judyhayun1102 3 жыл бұрын

is a point(that is not equal to zero) also a subspace? If we think of it as a position vector, it actually passes through the origin. that's why I'm curious

@diz8344 6 жыл бұрын

Thanks, it really helps me a lot.

@wesKokigen 13 жыл бұрын

THanks! It makes so much sense now.

@penuelraybantog5457 8 жыл бұрын

Perfect, thanks thanks. Perfect vid.

@_dkta 14 жыл бұрын

Wow...very well explained!

@techtalentblueprints 2 жыл бұрын

You are great. Now this concept is clear crystal for me.

@siddharthaganguly9286 6 жыл бұрын

Sal really enjoyed proving 0 vector is a subspace XD , great lesson as usual , keep doing it

@wonkamobil 14 жыл бұрын

Thanks a ton for the video, hopefully i'll pass my final because of this lol

@MsEwander 14 жыл бұрын

WOW, this is it!!! It's just great, thnx:)

@rahalrsh 12 жыл бұрын

great video! thanks..

@abdulrahman226 11 жыл бұрын

dude, Partrick is good and khan is good, they r different in their styles. khan is the very best in explaining the derivation and the origin of things, partick is gr8 in solving examples.

@dca24100 11 жыл бұрын

I feel ya. We're using that book here as well.

@legendkiller376 9 жыл бұрын

Khan you are a great man

@FakeAssHandsomeMcGee_ 11 жыл бұрын

Patrick is good no doubt. My only problem is that he just does the problems and tells you how to do it. With Khan, he explains why it happen. When I am doing my exams or homework, it just clicks and everything else just falls into place. Then I end up not seeing most of the other videos because I am able to "see" everything else. Hard to explain. I feel that with Patrick's, I will know how to do a problem, but will eventually get stuck and come back to his videos (good videos) again later.

@jaker9007 2 жыл бұрын

Best tutorials on linear algebra!

@trytwicelikemice7516 8 жыл бұрын

Trying to think in an abstract way about subspaces... could you say that a subspace is essentially an extension of the concept of an infinite line (1 dimensional) or plane (2 dimensional) into m dimensions, m

@trytwicelikemice7516 8 жыл бұрын

+LayZ K1D of course if m=n (not m

@shishenliart Жыл бұрын

I think of it as a subset being an open community of vectors whereas a subspace is a closed community of vectors. Since you can have a subset of Rn without it being closed under multiplication or addition or having the zero vector since it can span some or all of Rn. However, to get a subspace, you have to have it be in a subset that satisfies having the zero vector, closed under addition and multiplication.

@kushagrakalla7933 7 жыл бұрын

It helped a lot

@amangoel8724 4 жыл бұрын

thanks buddy you made my day

@empirewhite 7 жыл бұрын

Thank you, you are the best!

@marygraceadolfo8782 4 жыл бұрын

You're very kind, sir. Thanks

@sanyamyadav2806 10 жыл бұрын

GREAT IT IS.

@j0shda116 3 жыл бұрын

I was completely lost before watching only 25 seconds on this video. now I am a linear algebra prof

@mrdylanman666 14 жыл бұрын

Something just completely clicked. Thanks.

@Soccercrazyigboman 12 жыл бұрын

u know, I wonder why i even go to my math classes anymore... oh wait, potential attendance quiz and knowing what to look up on Khan

@sheralikhtk5200 4 жыл бұрын

thanks ALOT u saved me

@danielgibbons301 3 жыл бұрын

CLEARLY!

@yoursoothingmusic1754 2 жыл бұрын

thanks. you took 30 mins to to untwine the confusion my professor infused in me for one semester

@omertopchi2280 8 жыл бұрын

Thank you so much!

@Recordingization 3 жыл бұрын

Nice class!

@issaminasyan3143 8 жыл бұрын

Thank you Sal !!

@michellezhuang2483 4 жыл бұрын

For the example of whether U=span{v_1, v_2, v_3} is a subspace of R^n, don't v_1, v_2, and v_3 also have to have n components, as in they are a subset of R^n?

@michellezhuang2483 4 жыл бұрын

Other than that, your video helped clear everything up. Thank you!

@Crystalwaa 14 жыл бұрын

thank you so much!!!!! great explaination =D

@alexmickmusic 7 жыл бұрын

Thank you

@japierdoleokurwa 12 жыл бұрын

@123aellis in example (x1 in R and x1>0, x2 in R) this will be a subspace if any c that is in real set will satisfy above conditions. Your 'c' does satisfy condition -> v[2,4]*3=[6,12]. 6 is greater than 0. However -3 will product vector [-6,-12]. -6 does not satisfy condition x1>0. Important is that it must be valid for any c's in R.