General Rotation Matrix in 3D | Rodrigues’ Formula Derivation & SO(3)
8:23
YouTubeLet's Get Complex
General Rotation Matrix in 3D | Rodrigues’ Formula Derivation & SO(3)
In this video we explore rotations about the x, y, and z axes, the properties of rotation matrices (determinant, transpose, inverse), and how to construct the general rotation matrix for an arbitrary axis using Rodrigues’ formula. Finally, we connect these ideas to the special orthogonal group SO(3), an important non-abelian group in ...
4.4K viewsAug 20, 2025
Shorts
In 3D, rotation matrices are used to rotate objects around the x, y, or z axes. Each axis has its own specific rotation matrix. For example, rotating around the z-axis uses a matrix that leaves the z-coordinate unchanged but rotates the x and y coordinates, effectively spinning the object in the xy-plane. Similarly, rotating around the x-axis affects the y and z values, while rotating around the y-axis affects the x and z values. These 3x3 matrices are always orthogonal, meaning their rows and c
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In 3D, rotation matrices are used to rotate objects around the x, y, or z axes. Each axis
Mathswithmuza
A-Level Further Maths C3-24 3D Matrices: Deriving the General Rotation Matrices
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