What is a Subspace? [Passing Linear Algebra]

A subspace is just a collection of vectors that satisfies three special conditions.
Important theorem: All spans are subspaces! This should make sense if you consider how spans are defined; they meet all three requirements of subspaces!

[@thasneem-566]

YOU R TRULY A LIFE - SAVER. THE ONLY vid that explains things so clearly!!!!!!!!!!!!!!!!

[@julianceaser]

I tried to learn this with chatpgt. I thought the AI will explain it in a easy and fast way... at the end of the day it took me 3 hours with chatgpts help and it wasn't even correct. Your 10 min Video was the best explanation I found. Amazing. I hope, you uploaded a lot of videos in the same fast and efficient way about all other topics I will get in my Studies :)

[@Supercatzs]

It's unfortunate, but ChatGPT lies all the time. I tried teaching it some important concepts in Genetics and other Biology concepts, it understood the very basics; however, if you tried asking it to give you a hard question to formulate, it would just output answers that were not true at all. Same thing happened with math, it just doesn't know math.

[@cjjk9142]

Dont. use ai for maths, it's rubbish and gives a different answer each time

[@mrbanana6464]

@@cjjk9142 Exactly. I don't understand why people are praising AI for school. It's definitely useful for writing essays but for anything else that requires ChatGPT to give you information (instead of you giving information to ChatGPT and telling it to transform it in someway), it's absolutely useless.

[@erickrocha7972]

I watched so many videos and was about to give up, you saved me, thank you very much!

[@thibaultl1956]

A better explanation than any in my courses. Thank you dearly.

[@bigmoneymiller7174]

Thank you so much, no other videos helped at all; even the accounts that are usually on par with this one. Great work.

[@darkacademiavanessa]

i cannot thank you enough for this video because it is the only one on youtube that actually helped me understand this concept

[@luciaboljesikova1724]

I feel the same !!

[@spiderjerusalem4009]

try lin alg done right by axler

[@darkacademiavanessa]

@@spiderjerusalem4009 thanks but i'm done with linear algebra for life now haha

[@spiderjerusalem4009]

hehe i was too, but ye know preface exposure is seldom with intuition, rather with the traidition approach such as matrix & determinant in the preliminaries.
Axler's approach was pure algebraic (determinant in last chapter) as he thinks it's unintuitive. He made a youtube list th-cam.com/video/lkx2BJcnyxk/w-d-xo.html
Just some suggestion if you'd like. 😁

[@jamestanny849]

cap 🧢

[@yadalapavan9927]

youre the only one with actual good explanation in here now i understand this concept tysm

[@kingrobert7246]

Clear and concise, well spoken in a logical manner. Well done

[@phantasm3207]

Short and simple! Other videos drag this out. Thank you

[@dabeeramir1407]

This was a fantastic explanation, thank you so much!

[@grey5252]

Thank you soo much omgg. This is the only video which made me understand the concept

[@nicholaskong1673]

I needed a refresher. And it makes easy sense.

[@gavinp7692]

Great Explanation, simple.

[@kyew5173]

Very clever, thank you!

[@kaelwilson6947]

Thanks bro I appreciate the work you do

[@douyin-repost]

Of all the other videos, only you made it clear

[@precastdetailing]

THANK YOU SIR!

[@yotoad]

great explanation thank you

[@KylianMbappe07303]

you are A LEGEND!!!!

[@just4simplegg428]

Thank you very much ! It really helped

[@penmarking520]

keep it up these r great

[@jirapinyasiawsuk]

Thank you so much ❤

[@asagbajoseph4889]

Thank You Boss1!!

[@andrewthompson5755]

You the man fr

[@oscarsmathchannel]

great video thanks

[@user-wf3yb4jx8c]

So helpful!!!

[@aranganathan7112]

you made it easy

[@syabongajele6431]

thanks

[@akshitjain2906]

legend

[@boomperson818]

thank you

[@pradeepm701]

how a subspace is different from the larger vector space

[@thenutterjenny56]

WOW, HEAD BATTERED!!!

[@cagataytekin6372]

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[@alexsherman7414]

I love u

[@Someone_Named_GlowingSubspace]

I AM A SUBSPACE!

[@MathCuriousity]

Can someone explain why this is true
“Any line is affine. If it passes through zero, it is a subspace”. Why is ANY line “affine”?!

[@potatoballs7988]

idk man

[@littleameliapond]

if you're looking for information on. D/s subspace this isn't the right video.