Handling 3D transformations with matrices

 

 

 Rotation

 It is also possible to combine the three rotation matrices into one composite rotation matrix:

 Combine translation and rotation

Sometimes we want to combine translation and rotation so we can do both in one operation, but we can't do 3D translation with a 3x3 matrix, only with a 4x4 matrix, as defined below:

 

Properties of Rotation Matrix

 

Eigenvectors and Eigenvalues ​​of Rotation Matrix

Refer to the end of the link:

Maths - Matrix Transforms - Martin Baker