Base Change for Rotation: Example

This lecture discusses a rotation in 3D space with a given axis and angle, focusing on finding the image of a vector under the rotation. It explores the concept of changing bases for rotations, determining the matrix representation of the rotation in different bases, and understanding the orthogonal planes associated with the rotation. The lecture also covers the calculation of new basis vectors and provides examples of applying rotation matrices to vectors. Additionally, it delves into verifying rotation results and understanding the transformation of vectors under rotation.