Subspace

Showing something is a subspace of Rn by showing that it has the 0 vector, that it’s closed under addition, and it’s closed under scalar multiplication. Also showing R2 is not a subspace of R3
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[@HAL-oj4jb]

Very interesting video!
Didn't know that the R2 is not a subspace of R3 :)

[@carlosvargas2907]

En ese punto fue donde me perdí. A partir de hoy pensaré si es ese concepto el que no me deja avanzar...

[@dhunt6618]

Thanks for plowing through your subspace videos at warp speed!

[@sergiocampero3513]

Dr. Peyam, sus vídeos merecen más vistas. (Your videos deserve more views)

[@saitaro]

Linear algebra is beautiful, it starts trivial and seemingly simplistic, but eventually develops to such powerful instruments it blows mind. I read the classic Dr. Gilbert Strang's book and it was a real pleasure.

[@rockyjoe3817]

How come I didn't know you had a playlist in linear algebra? I will watch all of it!

[@chinesecabbagefarmer]

Great video, thanks for the upload! Looking good.

[@tinecrnugelj5253]

Watching this 4 hours before my Linear algebra final exam.

[@user-vd7nl7qn5b]

Thanks for your good videos. they are so good.

[@waqaracademy1821]

Outstanding sir

[@shinmengoxd4950]

Amazing video ♥

[@1willFALL]

For the closed addition in H, couldn't you have used both vectors u and v to be [x;y;0] so that when you add them it becomes [2x;2y;0] which is still of the form [x;y;0] but at the same time, you could factor out the 2...2[x;y;0] and show that c = 2 and also prove the closed scalar multiplication? Like kill two birds with one stone?

[@drpeyam]

Usually they’re different. c can be any real number, including things like square root of 2

[@MrRyanroberson1]

So i noticed a little trick. vertical * horizontal vector = matrix. Is there anything special about a matrix that pops out of this operation?

[@drpeyam]

Yep, check out my video on outer products

[@tabun76]

You mean subspace emissary lol

[@chinesecabbagefarmer]

I kept thinking the same thing!

[@user-bu8mg7uq3s]

thanks

[@wkingston1248]

Why does a subspace need to contain the 0 vector?

[@drpeyam]

In order for it to be nonempty. The empty set is not a subspace

[@izakj5094]

Since a subset has to be closed under addition and closed under scalar multiplication, if you take a vector v, calculate its additive inverse -v, then add the two you get something that has to be in your subspace. Which means 0 is in your subspace, since 0 = v + (-v).

[@JeremyGluckStuff]

Dr. Payem I disagree with your definition of subspace. When you define a subspace of a vectorspace as a subset of a vectorspace that is itself a vectorspace (with the same operations under potential restrictions), the "definition" you present comes out as a result of proving the vectorspace axioms generally for subsets.
Small point of contention, otherwise nice video 👍

[@suhailmohamed3013]

I learnt this in class... TODAY.

[@jjay6764]

Are subspaces of a system in Hilbert space real?

[@SmileyHuN]

If you show that taking 2 vectors and their linear combination is in H than H is a subspace, right?

[@SmileyHuN]

@Yo Ming sure

[@Davidamp]

@Yo Ming The zero vector is a linear combination of any vectors so it is in.

[@Zonnymaka]

Even (2,2,2) is a subspace...but not a linear/vector subspace. That was a pretty misleading video IMHO

[@drpeyam]

You’re confusing subsets with subspaces :)

[@Zonnymaka]

@@drpeyam I just realized that, unlike americans, we assign the "vector space" title only to linear spaces. All the other spaces are "affine spaces".