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

Understanding the definition of a basis of a subspace

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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.

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[Deuterium]

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.

[khanacademy]

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)

[elecengrmka]

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]

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

[danielgonzalezisaiev]

Dear Mr. Khanman,

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

[abhinavkumarsingh]

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

[mdib]

Everyone: His teaching is phenomenal.




Me: He always takes good colors. ✌😎

[mikohayle]

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

[MexterO]

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.

[Indianbutler]

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

[agentoranges]

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

[alastairzotos]

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

Seriously, you actually make it easy.

[STgauss]

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

[MaroLuva]

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)

[zoomboy]

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

[linleybaruch]

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 :)

[rochranomajeccavea]

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

[hadisyed]

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.

[tis_i_sana]

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

[keziah]

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