Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy

Подписаться 8 млн

Просмотров 1,2 млн

50% 1

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/line...
Understanding the definition of a basis of a subspace
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: ru-vid.com_...

Опубликовано:

8 окт 2009

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 208

@Deuterium52 8 лет назад

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.

@GameIsMyOxygen 7 лет назад

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

@Abdul_Rehman6162 6 лет назад

The best method of explanation. I cleared my Vector Space Concepts

@fermidirac8904 5 лет назад

math is not logical what are you saying

@khanacademy 15 лет назад

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)

@TrainPlaneBoat 6 лет назад

so u can span portfolios :o

@aviroxi 3 года назад

@@TrainPlaneBoat *spam XD

@meshachchacha6216 8 месяцев назад

@@TrainPlaneBoatyes

@elecengrmka 12 лет назад

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!

@RiarArt 12 лет назад

OMG i learned 10 times more in 19 min watching this video than in last 2 weeks of Linear Algebra classes at University xD

@nikitakundu2444 3 года назад

Couldn't agree more!!! I'm a 2nd time grad student and finally getting a grip on this topic!!

@danielgonzalezisaiev9643 11 лет назад

Dear Mr. Khanman, Thanks to you, I have realized that when I grow up I want to be LINEARLY INDEPENDENT!

@abhinavkumarsingh6319 7 лет назад

Thanks a ton from the bottom of my heart to make such amazing and outstanding videos.

@Indianbutler 8 лет назад

Thank you Sal:)! If only professors could explain and teach as you do. Again thank you so much for all the video

@MaroLuva 10 лет назад

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)

@mikohayle 13 лет назад

No one has explained this concept better than you! Thank you for all of your videos!

@agentoranges 7 лет назад

incredible. I took linear algebra last year and failed it hard. This time around, your explanations constantly make lightbulbs pop up in my mind.

@mdrakibhossain2433 2 года назад

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.

@MexterO123 13 лет назад

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.

@jeniferjanet4809 9 лет назад

You the real MVP

@mdib2001 4 года назад

Everyone: His teaching is phenomenal. Me: He always takes good colors. ✌😎

@alastairzotos 14 лет назад

You make math fun, because it feels good when everything just clicks in my head. Seriously, you actually make it easy.

@fuahuahuatime5196 10 лет назад

For real... I love how this guy teaches. Thank you so much.

@TravisLRoss 14 лет назад

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.

@STgauss3268 2 года назад

This is treasure man, why in the world have I missed your lectures all this time?

@zoomboy6676 2 года назад

All I can say is THANK YOU!!!!!!!!! You are the best prof for explaining linear algebra. Period

@allthingsacoustic 13 лет назад

Thank you for this video!! You just clarified a topic for me that had me completely lost.

@ruidechen 8 лет назад

Based khan academy! Finally understand this, not the abstract definition but actual examples and explanations :) If I only found you before my mid terms :(

@omerbirinci1691 5 лет назад

Thank you. Very clear explanation about relation between span and basis.

@sudupati 14 лет назад

Absolutely brilliant Sir. no more words to describe...

@Silhouette93 14 лет назад

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?

@ArchilonValdir 9 лет назад

Thanks for this! I really needed a refresher!

@dhruvbhati1347 3 года назад

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

@strwbrryshrtcke 14 лет назад

Thank you soooo much, this helped alot! You made it so easy to understand too

@jonathansweet2230 4 года назад

Thank you for helping me figure things out!

@keziah9798 3 года назад

hi, i just wanna say thank you for the video, it helps me understand better than my professor and my textbook

@rdzdrd0 10 лет назад

Khan saves the day again!

@Danfranschwan2 13 лет назад

you´re so an awesome teacher .... incredible

@rochranomajeccavea 11 лет назад

Thanks! i am absent for a week i our linear algebra class. :) So! thanks a lot! GODBLESS

@tuoyazhuo8063 6 лет назад

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...

@azrnzala 10 лет назад

great video to jog my memory :) thanks.

@fspopshovit 11 лет назад

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

@dawagyel 12 лет назад

thank you so much... u have always been life saver for me.. u are really the best

@mentld 12 лет назад

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? RU-vid doesnt show videos in correct order.. Anyways thanks so much and sorry for my english :D

@nasifhossain3441 3 года назад

The best video for understanding what the basis is!

@mrbriadis 3 года назад

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

@Ayplus 13 лет назад

@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.

@smhassanr 13 лет назад

i appreciate this so much, thank you khanacademy

@initrunlevel0 12 лет назад

thanks mr. khan, i am ready for linear algebra quiz tomorrow :)

@greenapplefever 14 лет назад

These are great videos. Excellent job.

@debasishkalita3962 7 лет назад

you are great sir, when you say about the last video,can you provide the link as well sir?

@3hz3zv4eey6v 12 лет назад

This is better than my professor, textbook, and classmates combined. Thank you.

@bjarktron 11 лет назад

I think my professor tries to make this as complicated as humanly possible with his explanations... thanks for the simplicity!

@elenaorins5284 5 лет назад

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

@tis_i_sana 2 года назад

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

@ullasrathodiitk5041 10 лет назад

its really great...

@elektronic 15 лет назад

saved my life man, thanks a bunch.

@norwayte 15 лет назад

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.

@hardtunesbigvibes 14 лет назад

thanks.great explaination

@Rovshenification 8 лет назад

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!

@josephdamen620 6 лет назад

You the man Khan

@MrMaarij 11 лет назад

God bless you good sir...God bless you...

@yarashamali8061 8 лет назад

his voice

@JetKMendoza 12 лет назад

Legend bro, keep up the awesome work! I think you should come teach at my university haha Definitely subscribed!

@Cliff86 10 лет назад

You should've mentioned that the basis of R^n will always only contain n vectors

@Sporky0000 9 лет назад

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.

@statushood 14 лет назад

great video!! thank you!

@GeekBoy03 12 лет назад

I wish there are links to previous and next video in a series

@sickpee 13 лет назад

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?

@irombebekanandameetei925 5 лет назад

Definitely i love ur videos sir.

@Maibes 13 лет назад

this guy rocks my world

@lhyx1990 13 лет назад

Every computer science student who wanna make awesome 3d games should definitely check this out. Best Linear Algebra tutorial ever!!!

@KhoaNguyen-jn1vr Год назад

thanks for your lecture a lot

@linleybaruch738 3 года назад

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 :)

@pubududarshana4883 Год назад

Thank You. You are great.

@FileMaker_Consultant 14 лет назад

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?

@denett01 11 лет назад

There is a linear algebra playlist with all the videos in order on his channel. This video is number 20.

@shmevanriceballz2857 Год назад

Thanks Sal. Saved my life

@khalidteama2441 7 лет назад

Amazing.... thanks you very very much!!!!!

@khalidteama2441 7 лет назад

Everything makes perfect sense now... spent all day trying to understand my lesson until I came across this. Cant thank you enough!!

@SuperStar-ql5cs 4 года назад

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.

@hongly1318 11 лет назад

omg...you've saved my life.........!!

@hadisyed1 11 лет назад

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.

@DocMaple8 14 лет назад

You, sir, are a godsend. And I'm not even religious. Thank you

@PwNStaaRR 12 лет назад

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!

@crumcon 15 лет назад

you know alot about math Khan

@janitarjanitar 14 лет назад

your the man Sal.

@MitzpatrickFitzsimmons 12 лет назад

isnt it then possible to define subsets of vector coords to infinity to and or of the the eleventy-seventh?

@kanishka475 10 лет назад

Thanks a lot.

@Helping.aspirant 5 лет назад

Thanks bery much

@denebgarza 13 лет назад

@khanacademy for work, or not for work. I'd still learn this. It's interesting.

@eda7210 4 года назад

Thank you so much sir

@Incrue 12 лет назад

Sal, you rock.There's a chance you make videos of electronics or mechatronics? Thank you very VERY much

@s4ms4r4 12 лет назад

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!

@damana1000 10 лет назад

Thanks alot

@DavidDouglasJr Год назад

I find this video much more enjoyable at 1.5X. Its ironic that this video is so redundant!!!

@Xlaxsauce 14 лет назад

your the man Sal

@JosephHarner 11 лет назад

That would be entirely to effective, logical, and cost-efficient for any university to consider implementing.

@oluwatoba11 13 лет назад

"In a Basis, you have no redundancy!"

@aniketpanda9302 4 года назад

Sir can you please make a video on finite basis and infinite basis with examples(especially polynomials).

@kingroy2377 14 лет назад

i am quite confuse about the basis, span, subspace..for example when you added another vector does it goes from R^2 to R^3, please can you explain ..thanks

@onewashere 12 лет назад

@TheGiglfoosm You have just described every one of my classes.

@ShanieMyrsTear 12 лет назад

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?

@evachao4890 2 года назад

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

@veryfrostyjack3067 Год назад

amazing

@danieldings1 11 лет назад

OMG Finally!

@Cyberpunk644 14 лет назад

never went to linear algebra class. cause prof sucks so bad.. you sir are the best!!!!!!!!!!!

@metalninjadragon 15 лет назад

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?