Basis of a subspace | Vectors and spaces | Linear Algebra

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

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14 жыл бұрын

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Understanding the definition of a basis of a subspace
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Пікірлер: 209

@khanacademy 14 жыл бұрын

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 жыл бұрын

so u can span portfolios :o

@aviroxi 3 жыл бұрын

@@TrainPlaneBoat *spam XD

@meshachchacha6216 7 ай бұрын

@@TrainPlaneBoatyes

@Deuterium52 8 жыл бұрын

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 жыл бұрын

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 жыл бұрын

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

@fermidirac8904 5 жыл бұрын

math is not logical what are you saying

@elecengrmka 12 жыл бұрын

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 жыл бұрын

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 жыл бұрын

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

@danielgonzalezisaiev9643 11 жыл бұрын

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

@abhinavkumarsingh6319 7 жыл бұрын

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

@jeniferjanet4809 9 жыл бұрын

You the real MVP

@Indianbutler 8 жыл бұрын

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

@mdib2001 4 жыл бұрын

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

@mikohayle 13 жыл бұрын

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

@MexterO123 13 жыл бұрын

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.

@agentoranges 7 жыл бұрын

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

@MaroLuva 10 жыл бұрын

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)

@mdrakibhossain2433 2 жыл бұрын

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.

@alastairzotos 14 жыл бұрын

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

@zoomboy6676 2 жыл бұрын

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

@fuahuahuatime5196 10 жыл бұрын

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

@STgauss3268 2 жыл бұрын

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

@TravisLRoss 14 жыл бұрын

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.

@ruidechen 8 жыл бұрын

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

@rdzdrd0 10 жыл бұрын

Khan saves the day again!

@jonathansweet2230 4 жыл бұрын

Thank you for helping me figure things out!

@keziah9798 3 жыл бұрын

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

@allthingsacoustic 13 жыл бұрын

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

@rochranomajeccavea 11 жыл бұрын

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

@yarashamali8061 8 жыл бұрын

his voice

@omerbirinci1691 5 жыл бұрын

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

@strwbrryshrtcke 14 жыл бұрын

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

@ArchilonValdir 9 жыл бұрын

Thanks for this! I really needed a refresher!

@nasifhossain3441 3 жыл бұрын

The best video for understanding what the basis is!

@3hz3zv4eey6v 12 жыл бұрын

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

@fspopshovit 11 жыл бұрын

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

@sudupati 14 жыл бұрын

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

@azrnzala 10 жыл бұрын

great video to jog my memory :) thanks.

@bjarktron 10 жыл бұрын

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

@Danfranschwan2 13 жыл бұрын

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

@dawagyel 12 жыл бұрын

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

@initrunlevel0 12 жыл бұрын

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

@tuoyazhuo8063 6 жыл бұрын

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...

@Ayplus 13 жыл бұрын

@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.

@greenapplefever 14 жыл бұрын

These are great videos. Excellent job.

@smhassanr 13 жыл бұрын

i appreciate this so much, thank you khanacademy

@josephdamen620 6 жыл бұрын

You the man Khan

@ullasrathodiitk5041 10 жыл бұрын

its really great...

@Cliff86 10 жыл бұрын

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

@Sporky0000 9 жыл бұрын

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.

@linleybaruch738 3 жыл бұрын

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 :)

@Rovshenification 8 жыл бұрын

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!

@SuperStar-ql5cs 4 жыл бұрын

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.

@Maibes 13 жыл бұрын

this guy rocks my world

@elektronic 14 жыл бұрын

saved my life man, thanks a bunch.

@hardtunesbigvibes 14 жыл бұрын

thanks.great explaination

@tis_i_sana 2 жыл бұрын

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

@MrMaarij 11 жыл бұрын

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

@mentld 12 жыл бұрын

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

@JetKMendoza 12 жыл бұрын

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

@statushood 14 жыл бұрын

great video!! thank you!

@mrbriadis 2 жыл бұрын

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

@lhyx1990 12 жыл бұрын

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

@norwayte 14 жыл бұрын

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.

@Silhouette93 14 жыл бұрын

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?

@pubududarshana4883 Жыл бұрын

Thank You. You are great.

@irombebekanandameetei925 5 жыл бұрын

Definitely i love ur videos sir.

@denett01 11 жыл бұрын

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

@khalidteama2441 7 жыл бұрын

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

@khalidteama2441 7 жыл бұрын

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

@hadisyed1 11 жыл бұрын

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.

@hongly1318 11 жыл бұрын

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

@dhruvbhati1347 3 жыл бұрын

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

@DocMaple8 14 жыл бұрын

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

@kanishka475 10 жыл бұрын

Thanks a lot.

@shmevanriceballz2857 Жыл бұрын

Thanks Sal. Saved my life

@KhoaNguyen-jn1vr 11 ай бұрын

thanks for your lecture a lot

@janitarjanitar 14 жыл бұрын

your the man Sal.

@debasishkalita3962 7 жыл бұрын

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

@oluwatoba11 13 жыл бұрын

"In a Basis, you have no redundancy!"

@damana1000 10 жыл бұрын

Thanks alot

@denebgarza 13 жыл бұрын

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

@s4ms4r4 12 жыл бұрын

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!

@Xlaxsauce 14 жыл бұрын

your the man Sal

@elenaorins5284 5 жыл бұрын

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

@JosephHarner 11 жыл бұрын

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

@eda7210 4 жыл бұрын

Thank you so much sir

@crumcon 14 жыл бұрын

you know alot about math Khan

@danieldings1 11 жыл бұрын

OMG Finally!

@GeekBoy03 12 жыл бұрын

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

@Helping.aspirant 5 жыл бұрын

Thanks bery much

@onewashere 12 жыл бұрын

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

@Incrue 12 жыл бұрын

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

@evachao4890 2 жыл бұрын

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

@blockbusstar 11 жыл бұрын

Bill Gates give this man another million dollars !!! The ART OF EDUCATION !!!

@vrchacho 13 жыл бұрын

@norwayte Computer graphics won't have gotten anywhere without this.

@catalinamaria9253 11 жыл бұрын

This Mr just saved my butt

@DavidDouglasJr Жыл бұрын

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

@kam1am 10 жыл бұрын

This is awesome, I'd be screwed w/o this video

@bobmuijs7401 11 жыл бұрын

You're a fraeakin' genius. I don't think I'm going to school anymore.

@kristkir 12 жыл бұрын

Great video, I feel like they should get rid of the useless lecturers and just play these videos in my algebra class.

@HK-sw3vi 4 жыл бұрын

I didn't give two shits about vectors when this was published, yet here I am

@metalninjadragon 14 жыл бұрын

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?

@veryfrostyjack3067 Жыл бұрын

amazing

@JesseDCrespo 12 жыл бұрын

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..

@sickpee 13 жыл бұрын

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?