Rotating Points Using Rotation Matrices

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! In this video I justify the formula used involving matrices to help find the new coordinates of a point after a counter clockwise rotation. There is one quick example as well at the end! The formula is pretty easy to use so long as your remember matrix multiplication so I spent more time on the justification part since it is more interested!

[@kseshan731]

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.

[@patrickjmt]

thanks for the kind words. good luck in your studies!

[@rickkay9548]

MAD respect doing explainers in SHARPEE. NO mess ups. Great work!

[@cheatman05]

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.

[@hoodiegamer9256]

We pay a million bucks in tuition but the guy from KZbin teaches way better for free OMG thank you very much Sir

[@patrickjmt]

hey! i have a name! :) glad you like the video :)

[@hoodiegamer9256]

@@patrickjmt no problem man. I appreciate you taking the time to teach this Patrick

[@AlexMcClung97]

Great explanation, thanks! It would be great to see a derivation of the 3D case (3x3 rotation matrix) also.

[@delandoduggan7698]

Please

[@vijaishankar3942]

​@@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]

@@vijaishankar3942 I need full answer for 3×3 matrix

[@susius4211]

@@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.

[@codebitcookie8053]

You just made my life easier, I can't thank you enough!

[@souraneelchattoraj1293]

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

[@varus7993]

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

[@yupitzmeeee]

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.

[@ian.ambrose]

@@yupitzmeeee That means you are very smart! Congrats!

[@veronicagonzalez5411]

thanks for all the help, you have saved me many times in my time of need and i just wanted to say thank you

[@keithturner1069]

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 :)

[@IrocZIV]

As always, a very helpful video.

[@fxckingjapanese]

Thank you so much Patrick!! I had an assignment of this. You almost saved my grade of Engineering Mathematics :D

[@mustafasiddiqui8203]

Almost?

[@yunweneric5528]

Quite eloquent and straight to the point. I find this quite helpful Thanks

[@imme.8736]

I love this video. It's super clear. Thank you a lot.

[@pathummudannayake6947]

Thank you. Awesome explanation. Some class just gave the matrix for 3D without saying how it got there. Your explanation is spot on.

[@sam90o48]

tysm for showing me this ,it will help me. in solving many problems

[@gidonkessler1799]

just what i needed for my programming :)

[@jonas26a]

Very helpful and explained well. Thank you

[@hartonianwar3607]

wow I like this video. very good at explaining the material

[@spicesmiles]

soo clear!! thank you!! no fancy tricks, just clarity...sigh again thank you!

[@kevinwest6611]

Spectacularly clear explanation! Thank you!

[@nabeelkamal92]

Thank you so much Patrick. Its great.

[@password6975]

Some of the best material on youtube

[@obensustam3574]

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.

[@dangkhanhlinh476]

This is exactly what i need. Thanks you

[@dr.sudharsanaraopotturu1380]

Excellent explanation, thanks for your efforts. Keep it up sir

[@TheCharbMusic]

Very good explanation, thank you very much !!

[@HabibKhan-jr9id]

Thanks. That was very helpful.

[@djgulston]

You are saving lives, sir!

[@mridulk81]

Made the topic so clear thnk u man

[@roycas3]

this explanation helped me a lot thanks.

[@JimmyGray]

Great demo!! Thanks!

[@marxregis]

Thank you for the great explanation!

[@gopinadhvuchuru1399]

Its a wonderful explanation Mr. Patric.... thanks man

[@ReversedFootage]

Absoluting amazing explanation, kudos!

[@domenicodifraia7338]

Great video man, thanks!

[@EverydaySimulations]

Love it if you'd do the 3 dimensional version! Thanks pat

[@mariamgarba1416]

thanks for this, is there a 3D (X,Y,Z) explanation of this videos?

[@ShahbazKhan-rg7fd]

Thanks man, really helped with understanding some Matlab code for my uni project

[@guy6567]

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

[@Haligonian]

You are shockingly good at freehanding straight lines.

[@ahsansher1059]

thanks for sharing it with us very nicely explained

[@Nicolas-Gonzalez]

Water clear explanation, thanks!

[@FreeMayaTutorials]

Amazing lecture! You are a great teacher.

[@patrickjmt]

Many thanks!

[@aramh3376]

Thank you mate.It's been useful.

[@weisu1427]

Thanks Patrick, this was really helpful!

[@patrickjmt]

perfect! glad i helped!

[@wisdom_wellness365]

Great explanation! Thanks

[@hi6747]

Thank you for your lecture.

[@avinashjha7848]

Thanks sir for this great explaination

[@gloystar]

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.

[@debarshiroy2939]

Thank you so much for the video

[@sitinurbaya6157]

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!

[@ghadoosh88]

YOU ARE A LIFE SAVER THANK YOOOOOOOOOOOOOOOOOU

[@rajeshramachander4799]

Fantastic explanation!

[@wellbangok8959]

I don't know why I'm here but DIFF EQ is a nightmare.

[@kemibello6812]

Very helpful, thanks

[@mutazkanaan6796]

thank you it help me , but if the rotation with clockwise ?

[@itsnotallrainbowsandunicor1505]

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.

[@ctobi707]

hello, thank you for the great video. can you please tell me if there is any difference between matrix rotation and euler rotation.

[@mathguy4264]

perfect. Thank you.

[@vestafarhan7580]

Really thank you 🙏 best teacher 👨‍🏫

[@galladeblade6001]

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

[@mistergun005]

Excelente explicación hermano se gano un seguidor.

[@adamtongi427]

Thank you very much. I didn't know how to represent a point in matrice form.

[@magicteen1]

This is gold!

[@lakshraja4831]

Thanks, great vid really helped me with the spinning donut

[@leah.2520]

thank you very much, i always wondered where this matrix came from !!!!!!

[@spoofvideo2361]

Hey friend, Very helpful video => Gret Perfect 2D Rotation.

[@mohamadhafizulazwanmohamad3333]

Great video. Very easy to follow.

[@patrickjmt]

Glad it was helpful!

[@tarikalansari5521]

amazing, thank you so much!

[@djamilahad9179]

Very useful thanks so much

[@kyawmaykhamon9711]

finally I can understand now thank you so much

[@geromeponch6248]

great video. thanks

[@marcovacante6614]

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)

[@izvarzone]

I wonder what kind of matrix would be needed for bend, taper or twist effect (in 3D)

[@nircoren8161]

amazing! thank you

[@lukas7966]

nice video! if you aren't interested in the derivation, start at 10:50 and for the "shortcut" start at 15:21

[@daqiangsz]

讲解很清晰，感谢

[@georginihrizov9317]

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!

[@davidnguyen4353]

thank you so much!!! my prof didn't show this on her slides

[@MuksEmmaN]

You explained in 9 mins what my lecturer tried explaining in a week

[@elnurvalikhanli7056]

thank you so much !!!

[@deependra5233]

Hey patrik, what about that physics tutorial you were to start? any update?

[@antonyraj9975]

Thank you so much

[@MuhammadSohailKhan]

its really helpful :)

[@lifematch]

Can you please do 3D rotational Matrices!!!!!! Honestly your way of teaching is the only way I can understand!

[@Promethinus]

If I change the rows of 2x2 rotation matrix, am I doing the same operation but in clockwise direction ?

[@CarlaLud]

Great explanation, thank you! But how would I change this method to rotate around an arbitrary point, instead of the origin?

[@krishpatel9139]

Add the value of the point to the end result.

[@MdAbdullahAlMuyid_nowho]

Thanks yo. A lifesaver : )

[@antonioworrell5524]

What if it was a clockwise rotation would you write negative 90 instead?

[@nooshax1]

thank you so much

[@electricengine8407]

my program actually works yay now i just need to figure out how to rotate vectors in 3d

[@felixwinchester9256]

have you done any video on calculator use?

[@frankmsigwa6674]

Thank you sir

[@dioutoroo]

Sheeeeshh!! You're excellent!

[@b0606089]

True content, no bullshit.

[@nhlavutelomacebele2336]

This is good Have you done it for 3D

[@kevinnguyen9703]

Thank you

[@dansedanse1173]

and for rotating in R3 is there a video?

[@taihatranduc8613]

thank you a lot