Transition Matrix for Axes Rotation in 3D and 2D - Linear Algebra

Learn how to transition between standard and rotated orthonormal bases in R^2 and R^3 using transition matrices for axes rotation. Explore the construction of transition matrices through trigonometry and apply rotation equations to express points in terms of rotated axes. Covers theorem on orthogonal transition matrices, rotation in 2D and 3D spaces, examples of axes rotation, and orthogonality. Includes timestamps for easy navigation through topics such as transition matrices, rotation equations, and practical examples in both R^2 and R^3.

Intro
Theorem on Orthogonal Transition Matrices
Rotation of Axes in 2-Space
Transition Matrix and Rotation Equations in R^2
Example of Axes Rotation in R^2
Rotation of Axes in 3-Space
Transition Matrix and Rotation Equations in R^3
Example of Axes Rotation in R^3
Orthogonality