Rotation matrix derivation (step-by-step prove)

👉 In this video we derive the Rotation Matrix that represents a coordinate transformation by rotation over an angle.

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#RotationMatrix #Stepbystep #Derivation

[PenandPaperScience]

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[liquidportal]

By far the best derivation for rotational matrices on Youtube. Excellent work.

[EnduroDEV]

Thank you, I was looking for exactly this kind of explanation.

[godslain]

Wow! Ive never heard anyone actually using the correct pronuciation for plus and beta like that! As an italian and a greek/latin student I really appreciate that!

[MOXTHEGAMER]

This is a wonderful video. I tried using my textbook to learn this, but this video made it so easy to understand. Absolutely love this video.

[breakdancerQ]

Didn't understand about cos/sin identities yet, but when I got that and came back to this I finally understand the derivation of this whole thing!

[ilredeldeserto]

so if I understand, here we want rotate a vector counterclockwise keeping the reference system fixed and so I have to use matrix in the video. But if I want keeping the vector fixed and rotate the reference system I have to use the inverse matrix of the matrix showed at the end because it's like to take the vector rotated in the new system and rotate it back clockwise. Is for this reason that there is confusion about where to put the - sign in the sen() of the matrix, it depends on what I want to rotate: the reference system or the vector. Am I right?

[ameliedzinka]

Finally, a normal explanation. Because everybody starts with a vector rotated from 0 angle.

[sonic-eedd]

thanks man, i study physics and they always used the rotation matrixes but they never explained them. Thanks a lot for the explanation now i understand how i can know if its an sin or cos.

[labloom]

Thank you, I am studying analytic geometry and this helped a lot

[MuhammadSadiq-gzgo]

I am very lucky to found this video what a good explanation

[mz]

Thanks for your video - you made it extremely easy to understand :)

[oussama]

Great explanation thank you very much for this video

[fifty]

makes a lot more sense to me now, thanks

[rajeshr]

It would be nice if you can make 3 dimensional matrix as well.

[Jenny-kqjv]

Hi, I love the video, but I have one question: when I change the x and y values of a function to xcos(b)-ysin(b) and xsin(b)+ycos(b) on Desmos graphing calculator, where b is the degree we want to rotate the function by, the function actually rotates in a clockwise direction instead of anticlockwise like shown in the diagram in the video, and I’m very confused about why?

[cdrqqjn]

really good video, thank you so much!

[barichm]

Why use trigonometric identities? The values in the matrix just represent the rotated axis. That is all you need.

The trigonometric values are of the angles with respect to the axis, not the point. That is why you don't need to calculate the distance.

The explanations I've seen of this are unnecessarily complex.

[mr.chindo]

in other videos the -sin theta is in 2nd row first column unlike your video where it is in 1st row second column.. any idea why?

[MohammadIsrar-ckqi]

In Virginia university slides....the trig identity of y' = r sin() sin() + r cos() cos()
And here is y' = r cos() sin() + r sin() cos()