Linear transformation examples: Rotations in R2 | Linear Algebra | Khan Academy

[@abhijit-z]

I never used to understand this but now after watching this video, I've clearly understood it.

[@boitumeloferdinandmatshidi4419]

Let me watch

[@saferehman8234]

Finally a channel that does eveything in a dark background xD

[@TheMrlightswarm]

I have a wonderful professor that clearly demonstrated this concept of coefficient matrices that is valid for rotational linear transformations but man Sal, you're the man for solidifying that knowledge! You've inspired me to teach and share the gift of knowledge and am currently pursuing a career in teaching mathematics! Thank you for all the help Sal. I want to let you know that your videos have left a positive impact in your audience's lives :). ~Cheers!

[@Anders.B.]

Jay P you just brightened my afternoon with your positive attitude. Hope you are having fun teaching!

[@norwayte]

I have read in a lot of textbooks different explanations of rotations - and yours is one of the best. Still waiting for - planes, points, lines and how they can relate to each other - Hessesche normal form - circles, ellipses and spheres - economic examples for matrix-multiplications - more on determinants...Sarrus....all the juggling with matrices to calculate real problems (examples) Keep on going.

[@ryanmonte]

For anyone that might have been confused by this... at around 1:55 when Sal says "what do we have to do to show that this is a linear combination?" I'm pretty sure he meant "what do we have to do to show that this is a linear transformation?"

[@JerryChenish]

I was looking for this for hours. Thank you for the explanation. It's pretty clear and I like your teaching vedio.

[@Cheech550]

Fantastic Video. If you have struggled to fully understand transformations in the past, then this video will ensure you have a keen working knowledge of Linear Transformations

[@apanapane]

This video helped me immensely to understand rotation matricies. I thank you, sir.

[@nwind27]

this is one of the super ultra clear lesson sal!!

[@LeVraiment]

Thank you for this video. I have a presentation on rotation transformation the next day. I must say this video has given me the right knowledge to present in class. Thanks a million times

[@spider853]

Thanks! Now its clear to me where those matrices are from... I'm programing 2D/3D games for 2 Years and never tried to figure out where did those transformation vectors comes.

[@anitharathod4770]

I didnt understand this topic in class....but now feeling its a really easy topic

[@zacklantz8181]

At last I understand this! I was pretty frustrated at first... about 15 videos later and I think I've got it!

[@aliusman9693]

thank you so much i was worried about these types of questions

[@AmarUllah-n2k]

Thank you Sal

[@ddsmax]

when u told us to ponder i started thinking bout vortexes and poverty, and now i own a million dollar business. atleast in my head.

[@GladnessGeorge-g5r]

Thanks alot for the amazing 😻😻 lesson it means a lot to me🎉🎉

[@FlareGunDebate]

This is a great description of linear transformation. Thank you very much.

[@WateryIce54321]

Always such fantastic explanations.

[@edoardolaspada]

Thank you very much, very clear explanation

[@vexedev]

I love you man!

[@TheJagdNinja]

So much better than my thick accented Russian Prof

[@s0m0c]

Thank you very much

[@Lena-si5fk]

Thanks, this video was very helpful! :)

[@aidenmurphy9924]

You use -sin because your angle goes past pi/2. What if 0 < angle < pi/2? Then it would be [cos sin, sin cos]?

[@NicoDevs1998]

Since e1 is always pointing up (since it is a basis vector), and since we rotate counterclockwise, e1 will never be in 0 < angle < pi/2. In the case where you over extend the angle, the angle will be greater than 270, the math will work out; for instance, the - sin (315) is positive sqrt(2)/2.

[@00165530]

Thanks!

[@Myrslokstok]

Love 6:24 where he states why.

[@HappyKitya]

5:48 16:40

[@arwaelkasaby471]

Really Thank you very much :3

[@SkubJohn]

Thank you

[@Waranle]

Another great video

[@s0m0c]

Gracias.

[@Morlich209]

Does the matrix also apply to rotations in the clockwise direction?

[@totoplopp6630]

Great information but please improve legibility, this is a mess.

[@THT1991]

@ryanmonte thx for bringing that up! i was hoping someone could make it clear for me and there you are =)

[@KAFA2020]

Awesome

[@marabi4]

why is the hypotenuse length 1?

[@sagarjagad6235]

Tysm sir

[@ramnareshdara5664]

Nice dp bruh

[@anurajdixit9707]

how to check linearity of rotation operators?

[@karimkhan1312]

You are excellent

[@yamacyurtsever7201]

Love you

[@fourelementmagicring]

what if i want to rotate it at certain point?

[@Judobrinez]

wat?

[@spdyeric]

@Roqu3ntin make it negative

[@junmun5035]

For the 26 people that disliked this vid... good luck because no ones gonna break it down like this for you.

[@thentust]

Why other films show the opposite sign of the Sin terms? but they explain also reasonable, but why has this difference?

[@thentust]

No,I was wrong. This one is to rotate the point,and the other one is to rotate the whole axises without the point. and cause the signs difference.

[@alexqiu3782]

The pace is too slow, good video though

[@melesebekele9015]

m

[@Zerpentile93]

Thank you. Now I do not have to read my poorly written fucking math book. :)

[@Dreaming-11]

This is not a proper demonstration, you skipped some important passages.

[@Jiao12]

Helpful as but could be much better. Stop being so ponderous!!

[@Gandalfbaws]

WTF!

[@DacoTaco]

@TheBatchGuy my math teacher was like that. i miss him so much :(

[@avishkadilshan1713]

Thank you!