Similarity Transformation & Class

 

These two idols are similar. The one in front can be transformed into the rear one exactly by replacing all the red & green stones with white stones.

Similarity Transformation is cited by the following expression,

X^-1 A X= B

Description: 

X^-1, A, X, B belongs to a mathematical group, G.

A is subjected to similarity transformation with respect to X.

B is the similarity transformation of A.

A and B are regarded as 'conjugate symmetry elements', The term 'conjugate' suggests 'similar'. And they belong to a class. Accordingly, the conjugate elements form a Class. In other words, A class comprises conjugate elements.