+ 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
5 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
5 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
5 жыл бұрын
ㅇㅇ
@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!
@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
7 ай бұрын
@@rahulkiroriwal8779 now 11
@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
@acのchannel
3 ай бұрын
factos
@dalisabe62
2 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.
@lolalukie713
12 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
3 жыл бұрын
@@lolalukie713 wow really great keep growing
@mihnea4924
6 күн бұрын
@@lolalukie713 how about now , you good ?
@Sundoren
10 жыл бұрын
superb voice superb explanation superb colors why we dont have teachers like u damn
@Hemenmyname
10 жыл бұрын
I personally am thankful for your service sir, thank you very 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...
inteusproductions Haha, he sure does, but none are given for teaching.
@neomarc9946
7 жыл бұрын
Thank you sir for making it 100% easier. My professor sucks af.
@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
14 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!!!
@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.
@Hepichack
10 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 !!!
@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!
@LAnonHubbard
14 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.
@snake10566
11 жыл бұрын
The way you define everything in simplistic terms is amazing. Thank you so much.
@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 :)
@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
@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?
@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.
@SoloPro
9 жыл бұрын
Seriously this explanation was good im so happy i typed it in youtube... defo liked and subbed
@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!
@swagatggautam6630
2 жыл бұрын
After watching this video I just have the urge to show this to my Linear Algebra lecturer and ask him, why his explanations are not this simple to understand?????????????????????????????????????????????????????????
@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
@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.
@beanfant_jesus
5 жыл бұрын
You taught me in 25 minutes what my professor took 2 hours to cover in class. Thank you!
@codingtheworld674
5 жыл бұрын
it is not the first time you have been facing like that a new subject, so that you understood in 25 min.
@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
@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
@judyhayun1102
4 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
@danielgibbons301
4 жыл бұрын
CLEARLY!
@deathmachine91
11 жыл бұрын
You are a better teacher than my professor. Thanks for putting the video up
@rapid1010
6 жыл бұрын
You're presentations are very clear and you're a great teacher as well.Thank you very much for these videos!
@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.
@Linkmarth
13 жыл бұрын
thank you so much
@preciousgeofrey6192
Жыл бұрын
More gratitudes should be granted to you Sir
@stephaniepaul2010
11 жыл бұрын
crazy to think i'm paying £9k a year tuition fees, but learn the course from these videos! Thankyou! :)
@mohammedsaeed4814
8 жыл бұрын
thanks
@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.
@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.
@123aellis
13 жыл бұрын
Question: Aren't the tests for closure for both scalar mult. and vector add. arbitrary? If you used c=3 for scalar multiplication, you would have had a new vector, still with x>0, and would answer that it is closed, and therefore is a subspace...? I'm having trouble getting my head around the idea of this...
@ocsantiago
14 жыл бұрын
This is great. I just discovered your library as well. Great stuff!!
@sarveshc2985
Жыл бұрын
wow what an amazing explanation! I spent too much time looking in notes and couldn't get much out of it
@AdamBr-q8d
Жыл бұрын
You are a life saver, thank you! I fully understand it now.
@AvengedRocker92
13 жыл бұрын
Really helped out, thanx for the video!
@MrSauce714
13 жыл бұрын
Linear algebra test tomorrow not worried about this topic thanks to you!!!! Great vid!!
@DEEPAKSINGHcreative
5 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.
@aandha1
13 жыл бұрын
This guy is just unbelievale !! Thumbs upp!!!
@예밤-f3k
3 жыл бұрын
this was such a great review before my first test
@aranyak1881
Жыл бұрын
Amazing, you teach 10 times better than my school does, god this world is weird.
@homestar92
13 жыл бұрын
These videos are teaching me more than my professor does. You may be saving my grade.
@yoursoothingmusic1754
3 жыл бұрын
thanks. you took 30 mins to to untwine the confusion my professor infused in me for one semester
@IndulgeObscenity
14 жыл бұрын
You are truly a great teacher! Than you for the posting!
@sharma1337
Жыл бұрын
is 0 considered neither positive or negative and thus can be classified as both when it fits your objective?
@eshaghazali2482
5 жыл бұрын
I have a quiz tomorrow God bless you sal!! 😭
@hariharann9930
Ай бұрын
just a doubt in the 2nd last example v1,v2,.v3 were threee random vectors in the coordinate system ?
@techtalentblueprints
2 жыл бұрын
You are great. Now this concept is clear crystal for me.
@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!
@Anonymoose123456789
11 жыл бұрын
A scalar is any number contained within the real numbers, which includes zero and every single positive and negative number. That also includes all of the fractions and decimals.
@nqvietanh343
13 жыл бұрын
If I have Khanacademy on youtube, what is the point of staying in my math class? Well, I have more time to study other classes! Yay!
@jasonjps
13 жыл бұрын
Is there a way to tell the order of all these videos other than date posted?
@rockclimbermaca
12 жыл бұрын
Salman Khan, the creator of Khan Academy, holds a bachelors degree in mathematics, a bachelors degree in electrical engineering and computer science, as well as a masters degree in electrical engineering and computer science from MIT, and an MBA from Harvard Business School. He is unbelievably talented, so instead of complaining you should be grateful for this amazing resource that you can implement in your education.
@rochelletarin6422
3 жыл бұрын
Well, this made more sense than my teachers lecture. Thank you!
@danielgonzalezisaiev9643
11 жыл бұрын
I'm learning crazy much! You already feel like my best friend dear khan academy mystery man.
@nturner4
14 жыл бұрын
wow this is awesome. this is SO much more helpful than any lecture I've been to this year!
@jaker9007
3 жыл бұрын
Best tutorials on linear algebra!
@j0shda116
3 жыл бұрын
I was completely lost before watching only 25 seconds on this video. now I am a linear algebra prof
@bigblockelectra
4 жыл бұрын
If you have a vector 'A' that goes out 10 units on the x axis and 'B' that goes up 3 units on the y-axis, and I go B+(-A) wouldn't that take you into quadrant 3? Isn't that outside the subspace?
@chvere123
14 жыл бұрын
it really saved me time for understanding these materials, thanks a lot.
@sharantheboss2957
4 жыл бұрын
But how is Span(1,1) closed under multiplication? You mentioned how any scalar multiplied by that vector would still be on the line but surely you would have to check whether a product of two vectors is still on that line (dot products generally aren't included in vector spaces say whaa)?
@multidarion
12 жыл бұрын
What if you multiplied the vector x at 16:18 by -1 like you did at 13:04 would it not be closed under scalar multiplication, just like the other one?
@marygraceadolfo8782
5 жыл бұрын
You're very kind, sir. Thanks
@Andradam33
14 жыл бұрын
Making up where my prof lacks - every time. Thanks for your useful explanations and videos.
@Adam-gp3ij
5 жыл бұрын
That’s pretty clear! Thank you
@violalagonigro-m4d
Жыл бұрын
Single-handedly saving my life
@TheRealChinOfKimJongUn
7 ай бұрын
This explained more in 20 mins (10 with playing it on double speed) than my college prof did in an 1.25 hrs...
@fathimahida8878
6 жыл бұрын
it really helped me... thanku soo much...keep uploading more vedios...
@zack_120
3 жыл бұрын
8:42 - To meet the 3 conditions as being a subspace means the vector contains ALL 0s, which means useless, or not?
@omertopchi2280
8 жыл бұрын
Thank you so much!
@zlsvr
4 жыл бұрын
12.06, should we write that a≥0 and c≥0 so a+c≥0 ?
@143hap
13 жыл бұрын
I won't say where I'm attending school, but geez, can you come teach here, I'm scrwed with these gtfs, well I have you so guess not, thanks brother, hope you get this,
@A-003
14 жыл бұрын
Thanks you VERY MUCH for the nice, simple, useful explanation. God bless you
@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
@sheralikhtk5200
4 жыл бұрын
thanks ALOT u saved me
@amangoel8724
4 жыл бұрын
thanks buddy you made my day
@thewiserone4112
5 жыл бұрын
Just wanted to ask at 11:00 why vectors were selected in only 1st and 2nd quadrant??
@wesKokigen
13 жыл бұрын
THanks! It makes so much sense now.
@dca24100
12 жыл бұрын
I feel ya. We're using that book here as well.
@diz8344
6 жыл бұрын
Thanks, it really helps me a lot.
@Bumperpegasus
13 жыл бұрын
And you are officially my new teacher
@bsvshashanka6055
3 жыл бұрын
wah!! superb video
@Recordingization
3 жыл бұрын
Nice class!
@timgoppelsroeder121
5 жыл бұрын
Thank you for these tutorials. They are very compact
@ishmaelteddy1454
9 ай бұрын
I didn't know you could scale a set of vectors by 0. I always thought your scaler should always be either a positive or negative number
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