Understanding Rotation Matrices

This video covers how to understand what a rotation matrix is and how it operates on the space.
I won't have any concept of angle or any trigonometric functions in this explaination. It is just to show you how the matrix works and how simple it is under the hood.
This example is for a 2x2 matrix (which can rotate a 2D space), but the same theory applies to a 3x3 matrix for a 3D space.

[naveenv]

Man you don’t believe how helpful this vid was for me to understand the concept….thanks buddy…

[davidschroeder]

Thank you! This was wonderful. I've been studying the weak interactions, and the CKM and PMNS rotation matrices play key roles in understanding how parity and CP violation are generated in the quark and lepton sectors, respectively. I really didn't exactly know what a rotation matrix was. I had a general idea, but this clarifies it completely, without the messy complications of trigonometry. I now see a clear pathway to being able to calculate the outputs of the aforementioned matrices from the actual numerical inputs. Just have to brush up on my trigonometry, which I took in school many decades ago.

[mhdimhdi]

thanks for sharing this it was very helpful

[movingshapes]

But on your example, not only you rotated, but translated too. That could be an undesired effect, like when trying to rotate a 3d model for 3d printing you end up positioning outside the printing bed. So can you show the rotation matrix for rotating around the center of the object? And let's say, 30 degrees, shall we? :)

[prezadent]

You are just avoiding "pulling sines and cosines out everywhere" because you are rotating 90 degrees.