Naming conventions in matrix diagonalization $ D = S^{-1} \cdot A \cdot S $

Question

The process of matrix diagonalzation is often summarized as

$$ D = S^{-1} \cdot A \cdot S $$

I understand that we often choose the first letter of the alphabet for the original matrix $A$ and $D$ for the diagonalized matrix. But where does the name of the matrix $S$ come from?

Answer 1

I would think $S$ here stands for similarity transformation.