Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy
ฝัง
- เผยแพร่เมื่อ 14 ต.ค. 2024
- Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
Understanding the definition of a basis of a subspace
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
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: www.youtube.co...
You are such a phenomenal teacher sal. You explain things more clearly than most college professors. Linear algebra is considered abstract to us undergrads, which it is, but you illustrate things so clearly. It reminds one that mathematics is rooted in logical reasoning and natural deduction. The way you explain things, everything is logical. So thank you very much for these videos.
Totally agree,he is one of the best teachers. Whenever i am confused about something,and if he has a video on it (which most of the time he has),by the end of the video it feels too easy. xD
The best method of explanation.
I cleared my Vector Space Concepts
math is not logical what are you saying
Most everyday jobs really don't require you to know what these things are. If you enter any scientific/academic field, the ideas of basis and subspace show up a lot. I've also had to use these ideas when I worked at a hedge fund (when we discuss "factors" that can explain movement of a portfolio--the factors are the basis vectors and the universe of potential portfolio performances is the subspace that it should span)
so u can span portfolios :o
@@TrainPlaneBoat *spam XD
@@TrainPlaneBoatyes
I could not understand anything in 6 classes of linear algebra in the university but few hours watching your clips have made everything crystal clear. May Allah bless you!
Thanks a ton from the bottom of my heart to make such amazing and outstanding videos.
Dear Mr. Khanman,
Thanks to you, I have realized that when I grow up I want to be LINEARLY INDEPENDENT!
OMG i learned 10 times more in 19 min watching this video than in last 2 weeks of Linear Algebra classes at University xD
Couldn't agree more!!! I'm a 2nd time grad student and finally getting a grip on this topic!!
I have an exam on wednesday, and with your help. I am confident in answering whatever my teacher gives in the Exam. This is was the first math class I actually was sort of lost in, and you have shown me the light. From now on your my teacher for higher level math.
Everyone: His teaching is phenomenal.
Me: He always takes good colors. ✌😎
You the real MVP
No one has explained this concept better than you! Thank you for all of your videos!
incredible. I took linear algebra last year and failed it hard. This time around, your explanations constantly make lightbulbs pop up in my mind.
That is the clearest definition of a basis I have heard in ANY college course I've had (including a whole semester of topology after linear algebra)
All I can say is THANK YOU!!!!!!!!! You are the best prof for explaining linear algebra. Period
You make math fun, because it feels good when everything just clicks in my head.
Seriously, you actually make it easy.
This is treasure man, why in the world have I missed your lectures all this time?
what tools do you use to create this videos? How do you make sure we can track your 'pencil' ? I'd love to use this for my online teaching. Thanks for sharing these videos btw! learned a lot from them
thanks mr. khan, i am ready for linear algebra quiz tomorrow :)
Thank you for helping me figure things out!
The video explains the subject matter very well. However, when solving for the vector equation @7:20 (or when determining if the equation has a trivial solution), I think it is better to use augmented matrix instead of plain equations...
Just a note: at 06:55 when he checks if they span R2 and then if they are linearly independant; this part is a little excessive. We can achieve the same thing by only checking if they are linearly independant and if they are then they must span R2
Thanks! i am absent for a week i our linear algebra class. :) So! thanks a lot! GODBLESS
I've got this in my finals tomorrow, and need to re-learn the whole topic because it's been a few years since I've last done it..
Thanks for this :)
What your doing is setting up simultaneous equations then solving them. Earlier we were using matrices to solve simultaneous equations. Can one use matrices and the determinant to see whether these are linearly independent?
Khan saves the day again!
Thank you Sal:)! If only professors could explain and teach as you do. Again thank you so much for all the video
his voice
Shame our world doesn't financially reward people who do such amazing work. Imagine, if he went to Goldmansachs making complex crazy market products he could make a lot more money!
hi, i just wanna say thank you for the video, it helps me understand better than my professor and my textbook
The lecturer is of Bangladeshi origin just like one of the co-founders of You Tube. That is one of the reasons why he is so good.
This is better than my professor, textbook, and classmates combined. Thank you.
Based khan academy! Finally understand this, not the abstract definition but actual examples and explanations :) If I only found you before my mid terms :(
I would gladly donate whatever amount you require to get the best tablet out there. So that you may continue to enrich our lives with your undeniable gift of teaching the most abstract and unwieldy concepts in the simplest manner.
基(basis)定義:
1. 可張成 subspace S 的向量
2. 線性獨立
作用: 可以用 basis 中向量的線性組合表示 subspace 中的任意向量
(是生成次空間的最小向量集)
PS: subspace 的 basis 不是唯一
The best video for understanding what the basis is!
You did a great job man.Fully understand the concept just in a few minutes which i didn’t in the whole last few years.
Thank you! This helps me so much :) The videos themselves are great but would it be possible for the episodes to be number-ordered or could quotes and such be linked to previous episodes? TH-cam doesnt show videos in correct order.. Anyways thanks so much and sorry for my english :D
You should've mentioned that the basis of R^n will always only contain n vectors
Thank you for mentioning this! I was wondering if the minimum number of vectors that forms a basis was 2, but now I see it depend on the dimension.
@norwayte . I think these r vital in higher level physics, engineering and vector calculus. I dont think anyone uses these 'day to day' unless u teach it @ a university but in advanced science fields when dealing with many variables and dimensions its necessary.
I think my professor tries to make this as complicated as humanly possible with his explanations... thanks for the simplicity!
Every computer science student who wanna make awesome 3d games should definitely check this out. Best Linear Algebra tutorial ever!!!
You, sir, are a godsend. And I'm not even religious. Thank you
Thank you for this video!! You just clarified a topic for me that had me completely lost.
Sal, just wanted to say thanks. I have been using these videos for understanding how to do singular value decomposition in my graduate level cognitive science course. This sort of stuff appears when modeling how the brain might process information retrieval and how search engine algorithms work. It is definitely not my favorite section of the class, because LA is conceptually hard if you have never seen it before. I am going to recommend these be included in our syllabus for future students.
There is a linear algebra playlist with all the videos in order on his channel. This video is number 20.
Thanks. That's what i wanted to hear. - Sounds like analogies of ideas. Even better - patterns of ideas which fit in every subject of human life. In this case... take something of something bigger, make assumptions about it, act with these assumptions and maybe you get a result that you can use for.. for instance to bring in more light in this "something bigger". Or anything else. Ideas are ideas are ideas. In this case they are mathematical...
Keep on going.
I'm a lazy to research something about Basis or anything about that but I think if I will watch your all lessons I will be lazy as always because everything is about linear algebra is in your channel. This is enough for me to do not any research about anything. Just click your channel and enjoy :D Thanks a lot!
Thank you. Very clear explanation about relation between span and basis.
I wish there are links to previous and next video in a series
Because I cannot find a video, is there a video on extending a basis?
Thanks a lot for the video by the way! My college hates using matrices
thank you so much... u have always been life saver for me.. u are really the best
you´re so an awesome teacher .... incredible
Great video, I feel like they should get rid of the useless lecturers and just play these videos in my algebra class.
For real... I love how this guy teaches. Thank you so much.
you are great sir, when you say about the last video,can you provide the link as well sir?
its really great...
Isn't it true that if we prove vectors v1 and v2 independent then it will automatically prove that they cover span R2, and vice versa? If so then we don't need to solve it 2 times
Absolutely brilliant Sir. no more words to describe...
From what I understand, you only need two in a plane basis, but a three dimensional basis would need a third vector, a four dimensional basis would need a fourth etc..
Thank you soooo much, this helped alot! You made it so easy to understand too
That would be entirely to effective, logical, and cost-efficient for any university to consider implementing.
These are great videos. Excellent job.
I'm not an advertise guy or anything for him, but! It just sounds like a lot of people who are watching this aren't aware that he has a site with all his videos nicely organised and whatnot ... Figured I'd pass it on, cause his videos have helped me in my math courses as well (calc, chem, alg, etc ...)
Just Google Khan Academy, and it's the first one that pops up.
saved my life man, thanks a bunch.
Thanks for these video's, they helped me a whole bunch! Too bad I found them so late, my exam is in 2 days! Keep up the good work though
@kingroy2377 basically, the vector is still in R^2 since it is a column vector with i and j components, thus making it two dimensional. The vector would be in R^3 if it were, for example, [2 3 1], since that has three components [i j k], rather than two components [i j], or [1 0] in this example
Thank You. You are great.
Sal, you rock.There's a chance you make videos of electronics or mechatronics?
Thank you very VERY much
thanks.great explaination
These are awesome, especially for a grad student in controls (yes another one) who is suddently smacked in the face with algebra symbols he hasn't seen in 10 years.
Why don't you mention the connection between linear independence and the determinent though?
your the man Sal.
@khanacademy for work, or not for work. I'd still learn this. It's interesting.
you know alot about math Khan
WHEN YOU SAY LAST VIDEO CAN YOU PLEASE PROVIDE A LINK TO THE LAST VIDEO!
If you go on their actual website it has them in order :)
www.khanacademy.org/math/linear-algebra/vectors_and_spaces
if you view the playlist it also has them in order
I find this video much more enjoyable at 1.5X. Its ironic that this video is so redundant!!!
Amazing.... thanks you very very much!!!!!
Everything makes perfect sense now... spent all day trying to understand my lesson until I came across this. Cant thank you enough!!
Sir can you please make a video on finite basis and infinite basis with examples(especially polynomials).
You're a fraeakin' genius. I don't think I'm going to school anymore.
God bless you good sir...God bless you...
great video to jog my memory :) thanks.
thanks for your lecture a lot
You the man Khan
Thanks for this! I really needed a refresher!
Got a question. If you have a 3x4 matrix and after row-reducing there are 3 pivot columns, leaving behind one free variable. Will it be a basis for R3?
your the man Sal
i appreciate this so much, thank you khanacademy
Question on the basis of a subspace. I see in this video we are using Basis' to find Spans. However, I don't see in the video how to find the basis itself?
Thanks bery much
"In a Basis, you have no redundancy!"
@norwayte Computer graphics won't have gotten anywhere without this.
Given a set of linearly dependent vectors, how would I determine which of those vectors I can "kick out" - so to speak - to get a basis for the space spanned by that set?
Legend bro, keep up the awesome work! I think you should come teach at my university haha
Definitely subscribed!
@TheGiglfoosm You have just described every one of my classes.
Great video. Just a little confused on how to know if they are generating system of R^2 or R^3 and whether they are bases of R^2 or R^3?
Can anyone answer please!
Why not use a more general term-Basis of vector space rather than subspace. BTW very helpful😇
This is 10 times better than my college professor
Question: If the set S is not linearly independent, you can still have a span V of it but it is not a basis, but if the set S is linearly independent, then the span of that particular set S is a subspace of V and it is a basis?
That is correct.
Yes Yes what you said is correct and important for better understanding
If the set S is not linearly independent meaning it is linearly dependent it can't be a basis for V but isn't it the span of S still a subspace of V?? It is just all the linear combinations of the vectors in V, so if V is a subspace wouldn't span(s) also have to be a subspace of V?
great video!! thank you!
Thanks Sal. Saved my life
never went to linear algebra class. cause prof sucks so bad.. you sir are the best!!!!!!!!!!!
Bill Gates give this man another million dollars !!! The ART OF EDUCATION !!!