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

Linear Transformation Examples: Rotations in R2

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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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[abhijit-z]

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

[saferehman]

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! 

[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?"

[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.

[apanapane]

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

[JerryChenish]

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

[nwind]

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

[anitharathod]

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

[aliusman]

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

[btbjmqm]

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

[Cheech]

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

[FlareGunDebate]

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

[spider]

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.

[zacklantz]

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

[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

[edoardolaspada]

Thank you very much, very clear explanation

[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.

[TheJagdNinja]

So much better than my thick accented Russian Prof

[Lena-sifk]

Thanks, this video was very helpful! :)