Lec 6 | MIT 18.06 Linear Algebra, Spring 2005

[michaela234]

a vector space inside a vector space....INCEPTION o.O

[jojoejoe]

Great professor... His students are very lucky to have him... My professors (during engineering) sucked big time...

[AntoMelta]

Good, I like that you share this video, I wish success always Column Space and Nullspace.

[willamricard]

Nice Video Column Space and Nullspace That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video Column Space and Nullspace From Your

[bundawartini]

Your Video Column Space and Nullspace Is Very Useful Sharing

[LnX53]

he emphasizes everything so good so that even the most idiots can understand... Great man !!

[LnX53]

this man deserves the money he get

[hsnbk]

I'm studying linear algebra in my own to take the challenge exam so Thanks for the lectures.

very useful and understandable

[MrFili3333]

This is really great and brilliant lecturer i never seen before. I like the methodology he is using and he knows how to engage his students.

I can see now how linear algebra is applied.

Thanks Gilbert Strang and MIT.

[SharylEloisrb704]

mmh guckt mich an bin ein elch

[aznpiccplayer123]

Finally someone who can explain image/range/column space clearly!!!

[awsomenesscaleb]

He wears the same shirt and same pants every lecture.

[mclaarson]

@awsomenesscaleb just as steve jobs rite? It doesnt mean a thing.

[allanjoshua84]

Dont dislike these videos for heavens sake... what the heck is wrong with you ppl???

[akhil089]

thanks professor strang

[SynthMelody]

A bit confused about the first part where he says that "P Union L" is not a subspace. Does he mean that the Union is not a subspace of P and not a subspace of L or that the Union is not a subspace of R^3? Because in my brain everything in the chalkboard is a subspace of R^3 :S

[he2he]

@SynthMelody The union is not a subspace. The union is bigger than P or L so it definitely can't be a subspace of either of them. and by adding a vector from P with a vector from U you can get to a point that is neither in P nor in U or in other words by adding two points from P∪L you can get to points outside of P∪L (somewhere in R³). But to form a subspace you have to be able to add any vectors from that subspace and the result has to be in that subspace.

[he2he]

@SynthMelody Maybe a simpler example helps. We take the X axis as one subspace and the Y axis as another subspace. So the union of those two spaces is all vectors on either axis, but nowhere else. For example (1 0 0) is on the X axis and (0 1 0) is on the Y axis. But the sum of the (1 1 0) is not on either of those lines. It's outside of it, so the union can't be a subspace, as otherwise you'd stay inside it when you add two vectors.

[pithikoulis]

@he2he Thank you man! That was a very good explanation :)

[tensorbundle]

He's a famous mathematician. Feeling privileged after watching his lectures.

[ClaytonOT]

I actually just took a formal linear algebra class at my university and it's crazy how the lectures are so similar. So I feel at least I'm getting a good education from my uni for a good price.

[hypnoticpoisons]

...what b turns out to b - lol

[jazzyb1030]

i should jus tranfer to MIT...like right now...

[hypnoticpoisons]

@jazzyb1030 that would be great, the problem is how..:D

[pedroissler]

Oe knows a truly good mathematician just by looking at how he carelessly overwrites stuff licentiously because it doesn't really matter. In his own words: "this is not Rembrandt, we're in linear algebra.."

[ChoEugene]

gosh. i want him to be my new lecturer.

i need an explanation using blackboard not projector

[WestWindBlowing]

intuitive

[SpoiledLogic]

i like my math professor and he is really smart, but he doesn't explain like this. he expects us to get it just by him writing down theorems. I like Strang's intuitive approach to understanding vector spaces. I wish i went to MIT

[Heretic3030]

I like how he calls vectors or columns "this guy" and "that guy"

[cool4skull]

17:10 "you can see from the way I am speaking what the answer is going to be..."

--wish my profs spoke like him...

[UncleBards2]

what a don! i wish my lecturer was this guy, he makes it so simple

[sdcororaton]

Terrific, terrific lecture, esp his way of using linear combination / "column picture" to solve equations. I have never heard of it, but it is so much easier! Thank you Prof. Strang/MIT for posting these lectures!

[sdcororaton]

Terrific, terrific lecture, esp his way of using linear combination / "column picture" to solve equations. I have never heard of it, but it is so much easier!

[KaLNFoRc3R]

i finally learn something

[MADLmaan]

those MIT blackboards are like Hogwarts...secret boards out of nowhere

[subash3]

HELP! I think Strang might have got WRONG around 05:40. I think P U L is a SUBSPACE of P as P & L itself is a subspace of P.

Think like this: let p & l be a vector from P & L respectively. than u=p+l belongs to

P U L and u lies within P as p is within P and l is also within P.

Also c*p & c*l belongs to P & L respectively where c is scalar as P&L are subspace. so c*u=(c*p + c*l) belongs to P U L.

Finally, zero vector lies in both P & L. so Zero vectors belongs to P U L.

So P U L is subspace.

[Santakingkong]

@subash3 I think P U L is a subspace only in line L lies in the plane.

[subash3]

@Santakingkong i don't get what ur saying but Thnx.

Anyway, i think i may have found the solution.

When he was talking about line L, i thought L was a subspace of P (also his diagram of L kind of looks like L is inside P) . If it was, than P U L=P & P itself is a subspace of P.So P U L is a subspace of P.

But if he was talking about L that passes through orgin but doesn't lies in plane P (so L penetrates P), than ofcourse P U L will not be subspace of P.

So my interpretation of L was wrong.lol

[reid300]

awful course!

[Reggae4Triceratops]

@reid300 ya bur he teaches it well

[Pranikki1]

He's much better than my lecturer at the LSE.

[pcbjunkie]

this guy is awesome the proffs at the university of toronto dont know shit abt math...

[SHEMANROBOCOP]

i would give this guy a standing ovation, these mit punks dont know how bad other professors can be

[CBeerzy]

is this who kevin spacy was supposed to be in 21? haha

[awesomeous20]

He explained in 1 lecture what took my professor 3.... very good teacher

[Cherubinpri]

lots of help!

[gsmsteve]

great video!

[roombaba]

@Aerosion No one has any questions since Dr. Strang is that awesome

[maxlyger]

man. I finally understand it.

[KarlCrack]

Shizzle! He forgot his neck tie!

[xploi]

Finally the subtitles are on sync!!

This is great!!

[Kyrgyzstudent]

Thank You very much for such marvellous courses!

[DaWanderer]

Why is it necessary that the subspace P or L of R^3 must go through the origin [0,0,0]???

What if this plane P doesn't go through the origin? Isn't it still a subspace???

[falcord]

Any subspace must contain vector (0,0,0), otherwise, if you do w*0 the answer would not belong to the subspace.

If the plane doesn't go through the origin, it's not a subspace.

[khatmandu89]

@DaWanderer he says the origin must be contained in any subspace because multiplying any vector by 0 will give you the origin.. and that is the scalar multiplication rule.

[mathgoddess64]

@khatmandu89 If it is a subspace then the scalar multiplication will hold therefore zero vector is contained.....If it is not a subspace then the scalar multiplication will NOT hold so you could not force the zero vector to be contained.

[glentellefsen]

22:49 - what b, turns out to b .. :-) Great lecture, occasional pokes of humor and self irony is great!

[aleant]

AMAZING Lecturer! Easy steps to follow and talks slow enough to understand. Thank you MIT!

[simonjiang12355]

much better than my prof ! I like him

[Aerosion]

not one person has a question in any of these? wtf

[8cccpeevostokzempf]

I know--they're sitting there like bumps--I gave him a standing O at the end of Lecture 4. Bravo !!!

[8cccpeevostokzempf]

Oooops--I meant Lecture 5--get confused by all the Big Numbers s-times. Lecture 5Standing O--Lecture 4 Bad Sound.

[osiumjrtosfyo5syerg]

maybe because of its simplicity... it's obvious!

[chandigarh47]

Ax =b, never understood this thing better than this before..

[harish400]

39:36. haha... this guy is a genius

[positrongamma]

he is a great mathematician

cheers

[MrSystemVI]

Excellent lecture! Thanks!

[raymyster2]

Dr Strang that's a great lecture right here!

[turcorox911]

GILBERT STRANG FTW!

[nitheshp1985]

awesome...really helpful

[jcarol555]

I love the rating for this comment.

[Laiquelleion]

I think many of the videos has been updated recently to a better quality though. So the views of the previous video may not show anymore.

[Mathematics215]

Lol i like how the number of views decreases with the lecture number.

[tondominguez]

lol, that is so true

[Treesrule14]

Its because people are in the middle of viewing the videos

[lhaussmann]

yeah... why do u think that happen?

[aaronarmstrongskomra]

The audio is messed up on this one.

[126altf4]

no kidding