Rotation Matrix

Derivation of the rotation matrix, the matrix that rotates points in the plane by theta radians counterclockwise. Example of finding the matrix of a linear transformation

[blackpenredpen]

A pic is worth 1000 words, just like the thumbnail!

[jdmc]

You are a Maths Angel that has come to earth to teach us poor Maths disciples...Love your lectures- A massive heartfelt THANK YOU

[Crimson_Thief]

Dr. Peyam is a miracle worker! The differentiation trick is so useful!!!!

[alpmuslu]

i cant put in words how much this has helped me, thank you

[SquishySwishy]

Such a simple concept, couldn't find a legit explanation anywhere! thank you!

[bikeman]

You sir are a lifesaver and have deserved a subscription! I'm currently in Linear Algebra and Matrix Theory, and have been struggling with this concept. Your video was just the information I needed and you seemed very enthusiastic to present it. Keep up the great work 👍

[mitchkovacs]

Another great application of this is in proving the angle sum identities. For angles alpha and beta with respective rotation matrices A(alpha) and A(beta), we know that multiplication by A(alpha)*A(beta) must be identical to multiplication by A(alpha+beta). So after multiplying out A(alpha)*A(beta), the angle sum identities for both sine and cosine just fall right out.

[officiallyjk]

You my good sir saved me so much trouble. I was writing a raycasting algorithm and was struggling at rotating the vectors. This video provided a crystal clear explanation on rotation matrices. Thanks so much!

[postnubilaphoebus]

Just wanted to let you know that you are an awesome teacher. Whenever I want to clear up a mathematical topic I encounter during my studies, I watch your videos.

[GamaSennin]

The rotation matrix is so cool! I like how you can apply it to itself to get _another_ rotation of θ, which is just a total rotation of 2θ, and the matrix multiplication will lead automatically to cos 2θ = cos^2 (θ) - sin^2 θ and sin 2θ = 2sinθcosθ. Also, I don't remember ever learning that differentiation and determinant rule to check the columns; that was awesome!

[atalantaquattrocchi]

Thank you so much for this simple and clear explanation. Please, never stop what you are doing, your videos are life changing.

[neoblackcyptron]

Super awesome explanation. Thank God for YouTube preserving live knowledge for posterity. This is a living library the university of the universal swarm mind.

[ifra]

Why don't our university professors teach like you? 😢
I am blessed to have this channel.

[-anonim-]

Thanks a lot! I'm fronted developer and your information helped me!)

[ProletarianNuklearWarrior]

I looked through so many videos and this is a godsend! THANKS A LOT!!

[MrRyanroberson]

i like the fact that there are two different ways of inverting the rotation matrix: first by the "pepper grinder", a matrix (a, b, c, d) has the inverse (d, -b, -c, a)/(ac-bd), and ac-bd in this case = 1, and the result just negates all sin(θ). the other solution is the "geometric" truth that you can just plug in the opposite value, since applying rotations is additive to the input, but sin(-θ) = -sin(θ)

[jyotiranijyotirani]

He'll I am india I watch your video first time and it is very helpful for me

[AbdulMoiz-ujwg]

Thank you Dr peyam, I really needed this.

[thestovietunion]

Thank you, I thought I knew matrix multiplication (turns out I forgot) and was frustrated by how the 3 dimensional rotation ones just don't add up for me, now I understood that something was wrong with it and looked it up, now they make more sense to me (as I got matrices of 3 x 3 as coordinates of a point living in a 3 dimensional space, and those coordinates definitely aren't a 3 x 3 matrix).

[patmull]

Why the hell nobody actually explains this? Every time it goes like this: here is the rotation matrix. Sinus, cosine simple. Next slide. And I was always confused. Sin what!? Why even cosine in the first place? Why there is a minus sin? Why the heck (I would like to use more explicit language) can't somebody explain it like this guy above. Thank sgod for this man!