Hi all! Wanna help a TH-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
I am a chemist (retired professor) and I am trying to understand how animation works (matrices and graphics). You are a wonderful teacher. Thanx for helping me to come to this solution for rotating vectors using mathematics I learned at school (and remember still). Brilliant lesson.
Finally I can think of something when someone says "transformation matrices", because those were nothing but a bunch of vectors for me till now. Thank you for making this great, clear explanation.
I watched your videos since I was an undergraduate student, now I am studying in Ph.D and still watch your videos XD. Thank you so much for everything you have made for us. I am really appreciated
@@delandoduggan7698 It's the same for 3D, here we are rotating along the z-axis, so if you want to rotate along the y axis then substitute x and y with x and z. So it's just a matter of changing the axis.
@@dhanush.n290 the Z stretches out of the plane, so rotating the other two does not affect it. Therefore, you would append a Z’(0) to the end of the pre-existing equations. For the third equation, you are rotating/performing transformations with the Z-axis directly, not the other two. Therefore, they are x’(0) y’(0) by the logic used previously. Z would be Z’(1) because it is now being transformed.
I am a robotics software engineer and use rotation matrix for differential robot position estimation in my code. However, I was not aware of the mathematics behind it. Thank you so much for this great explanation.
Dude you have no idea how much this video helped me understand the -sin theta, i forgot about trig identities and this is just what I needed to carry on my 2 link manipullator research. Thank you
Hey mate, I'm currently doing a mathematical exploration of matrices as part of a teaching degree. I stumbled upon the rotation matrix through some guess work, but I didn't understand where it came from until your video, what a great explanation! I would have never gave thought to use that trig identity. Cheers and keep up the good work :)
never thought id need this so when i learnt in school i didnt understand, now i need it for my code, funny how that works, im so interested this time, last time didnt even care enough to remember
Dude, you're the best! This is indeed the best and simplest explanation and derivation of that rotation matrix. Other guides on the net just complicate things. I love your videos. Perhaps you could make a video demonstrating how, using this formula, the y=1/x curve is actually the hyperbola [(x^2)/2 - (y^2)/2 = 1] rotated 45 degrees counter-clockwise.
I was able to work it out after the half way mark, but thank you. The way it's taught in books left me wanting more. I never felt it was properly explained. Was it sin(theta) or -sin (theta). Utilizing trig identities, it explains where one places the minus sin.
Awesome video! very clear explanation ...thank you so much ! would like to ask... how do you get the left side matrix if you know the initial and final coordinates... thank you so much!
Can you solve this: The linear transformation Tθ corresponding to counterclockwise rotation in the plane through an angle θ has standard matrix: cosθ −sinθ sin θ cos θ Use the appropriate matrices of this type to show that the composition of the transformations corresponding to counterclockwise rotations by 30◦ and 60◦ is equal to the transformation corresponding to counterclockwise ◦ rotation by 90 . I have no idea how to approach this. It’s a practice problem in my class.
I can't do matrix notation on here of course, but it's quite simple. Call your rotation matrix by 30 degrees A and your rotation matrix by 60 degrees B. Designate by C the rotation matrix for 90 degrees. What you have to show is that the matrix product BA = C, which you can do by good ol' plug and chug.
Hi all! Wanna help a TH-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
I am a chemist (retired professor) and I am trying to understand how animation works (matrices and graphics). You are a wonderful teacher. Thanx for helping me to come to this solution for rotating vectors using mathematics I learned at school (and remember still). Brilliant lesson.
thanks for the kind words. good luck in your studies!
MAD respect doing explainers in SHARPEE. NO mess ups. Great work!
Finally I can think of something when someone says "transformation matrices", because those were nothing but a bunch of vectors for me till now. Thank you for making this great, clear explanation.
I watched your videos since I was an undergraduate student, now I am studying in Ph.D and still watch your videos XD. Thank you so much for everything you have made for us. I am really appreciated
I am like 15 years old and in my country this comes in when you’re like 17. And I am still doing it lmao.
@@yupitzmeeee That means you are very smart! Congrats!
Great explanation, thanks! It would be great to see a derivation of the 3D case (3x3 rotation matrix) also.
Please
@@delandoduggan7698 It's the same for 3D, here we are rotating along the z-axis, so if you want to rotate along the y axis then substitute x and y with x and z. So it's just a matter of changing the axis.
@@vijaishankar3942 I need full answer for 3×3 matrix
@@dhanush.n290 the Z stretches out of the plane, so rotating the other two does not affect it. Therefore, you would append a Z’(0) to the end of the pre-existing equations. For the third equation, you are rotating/performing transformations with the Z-axis directly, not the other two. Therefore, they are x’(0) y’(0) by the logic used previously. Z would be Z’(1) because it is now being transformed.
Thank you so much Patrick!! I had an assignment of this. You almost saved my grade of Engineering Mathematics :D
Almost?
nice video! if you aren't interested in the derivation, start at 10:50 and for the "shortcut" start at 15:21
I am a robotics software engineer and use rotation matrix for differential robot position estimation in my code. However, I was not aware of the mathematics behind it. Thank you so much for this great explanation.
soo clear!! thank you!!
no fancy tricks, just clarity...sigh
again thank you!
You just made my life easier, I can't thank you enough!
Dude you have no idea how much this video helped me understand the -sin theta, i forgot about trig identities and this is just what I needed to carry on my 2 link manipullator research. Thank you
Quite eloquent and straight to the point.
I find this quite helpful
Thanks
Hey mate, I'm currently doing a mathematical exploration of matrices as part of a teaching degree. I stumbled upon the rotation matrix through some guess work, but I didn't understand where it came from until your video, what a great explanation! I would have never gave thought to use that trig identity. Cheers and keep up the good work :)
never thought id need this so when i learnt in school i didnt understand, now i need it for my code, funny how that works, im so interested this time, last time didnt even care enough to remember
thanks for all the help, you have saved me many times in my time of need and i just wanted to say thank you
You are shockingly good at freehanding straight lines.
Thank you. Awesome explanation. Some class just gave the matrix for 3D without saying how it got there. Your explanation is spot on.
We pay a million bucks in tuition but the guy from TH-cam teaches way better for free OMG thank you very much Sir
hey! i have a name! :)
glad you like the video :)
@@patrickjmt no problem man. I appreciate you taking the time to teach this Patrick
Dude, you're the best! This is indeed the best and simplest explanation and derivation of that rotation matrix. Other guides on the net just complicate things. I love your videos. Perhaps you could make a video demonstrating how, using this formula, the y=1/x curve is actually the hyperbola [(x^2)/2 - (y^2)/2 = 1] rotated 45 degrees counter-clockwise.
Made the topic so clear
thnk u man
You explained in 9 mins what my lecturer tried explaining in a week
Some of the best material on youtube
Amazing lecture! You are a great teacher.
Many thanks!
Spectacularly clear explanation! Thank you!
I was able to work it out after the half way mark, but thank you. The way it's taught in books left me wanting more. I never felt it was properly explained. Was it sin(theta) or -sin (theta). Utilizing trig identities, it explains where one places the minus sin.
You are way better at explaining this than Khanacademy. Praise the lord!
Thanks man, really helped with understanding some Matlab code for my uni project
I love this video. It's super clear. Thank you a lot.
I have been banging my head the whole day trying to rotate a triangle and if it were not for you I would have lost my sanity. Thank you!
Really thank you 🙏 best teacher 👨🏫
Its a wonderful explanation Mr. Patric.... thanks man
Water clear explanation, thanks!
Thanks, great vid really helped me with the spinning donut
Thank you very much. I didn't know how to represent a point in matrice form.
Excellent explanation, thanks for your efforts. Keep it up sir
Very very helpful seriously very helpful thankyou so much, i was working on an HTML canvas project and this helped me alot
glad it helped :)
You are saving lives, sir!
Absoluting amazing explanation, kudos!
As always, a very helpful video.
Great video. Very easy to follow.
Glad it was helpful!
Thank you mate.It's been useful.
Can you please do 3D rotational Matrices!!!!!! Honestly your way of teaching is the only way I can understand!
Thank you for the great explanation!
just what i needed for my programming :)
thank you very much, i always wondered where this matrix came from !!!!!!
Fantastic explanation!
tysm for showing me this ,it will help me. in solving many problems
I don't know why I'm here but DIFF EQ is a nightmare.
Thank you very much, very good explanation!
thank you so much!!! my prof didn't show this on her slides
Great explanation thanks fella
True content, no bullshit.
this explanation helped me a lot thanks.
wow I like this video.
very good at explaining the material
Thanks sir for this great explaination
thanks for sharing it with us very nicely explained
finally I can understand now thank you so much
Very helpful and explained well. Thank you
Very good explanation, thank you very much !!
YOU ARE A LIFE SAVER THANK YOOOOOOOOOOOOOOOOOU
This is exactly what i need. Thanks you
Great explanation! Thanks
Thanks Patrick, this was really helpful!
perfect! glad i helped!
Thank you so much Patrick. Its great.
Thank you for your lecture.
Thank you so much for the video
Love it if you'd do the 3 dimensional version! Thanks pat
thanks for this, is there a 3D (X,Y,Z) explanation of this videos?
Sheeeeshh!! You're excellent!
Great demo!! Thanks!
This is gold!
When - sin is in the second row, that makes a clockwise rotation.
When it is in the first it will be counter-clockwise.
Great video man, thanks!
Bull eyes explanations dude you have logic great
Excelente explicación hermano se gano un seguidor.
Nice video for my surface orientation system from game character on slope. I love trigonometrics 7w7
Great explanation, thank you! But how would I change this method to rotate around an arbitrary point, instead of the origin?
Add the value of the point to the end result.
Thanks. That was very helpful.
amazing, thank you so much!
Awesome video! very clear explanation ...thank you so much !
would like to ask... how do you get the left side matrix if you know the initial and final coordinates... thank you so much!
my program actually works yay
now i just need to figure out how to rotate vectors in 3d
great video. thanks
Very helpful, thanks
Thanks buddy
Hey friend, Very helpful video => Gret
Perfect 2D Rotation.
hello, thank you for the great video.
can you please tell me if there is any difference between matrix rotation and euler rotation.
have you done any video on calculator use?
If I change the rows of 2x2 rotation matrix, am I doing the same operation but in clockwise direction ?
amazing! thank you
how would you do the problem at 14 minutes for a vector in R3. like if i had rotation for something about (-1,-1,-1)
and for rotating in R3 is there a video?
讲解很清晰，感谢
thank you it help me , but if the rotation with clockwise ?
sir .. will you talk about rotation matrix in 3D .. (x,y,z)
yeah I'd like to know about that too!
Awesome Buddy.
Hi sir Patrick. can you show me your recording setup? I have a reporting tomorrow that requires a video and I want to do a vid like yours
I wonder what kind of matrix would be needed for bend, taper or twist effect (in 3D)
Thanks yo. A lifesaver : )
Can you solve this:
The linear transformation Tθ corresponding to counterclockwise rotation in the plane through an angle θ has
standard matrix:
cosθ −sinθ
sin θ cos θ
Use the appropriate matrices of this type to show that the composition of the transformations corresponding to counterclockwise rotations by 30◦ and 60◦ is equal to the transformation corresponding to counterclockwise
◦
rotation by 90 .
I have no idea how to approach this. It’s a practice problem in my class.
I can't do matrix notation on here of course, but it's quite simple. Call your rotation matrix by 30 degrees A and your rotation matrix by 60 degrees B. Designate by C the rotation matrix for 90 degrees. What you have to show is that the matrix product BA = C, which you can do by good ol' plug and chug.