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The Cayley–Dickson construction is closely related to the [[regular representation]] of '''C''', thought of as an '''R'''-[[Algebra (ring theory)|algebra]] (an '''R'''-vector space with a multiplication), with respect to the basis {{math|(1, ''i'')}}. This means the following: the '''R'''-linear map
:<math>\begin{align}
\mathbb{C} &\rightarrow \mathbb{C} \\
z &\mapsto wz
\end{align}</math>
for some fixed complex number {{mvar|w}} can be represented by a {{math|2 × 2}} matrix (once a basis has been chosen). With respect to the basis {{math|(1, ''i'')}}, this matrix is
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