A second instance involves functions of a motor variable where arguments are split-complex numbers.
In mathematical physics, there are hypercomplex systems called Clifford algebras.
A matrix may be considered a hypercomplex number.
For example, the study of functions of 2 × 2 real matrices shows that the topology of the space of hypercomplex numbers determines the function theory.
[1] The function theory of diagonalizable matrices is particularly transparent since they have eigendecompositions.
Then the function theory is enriched by sequences and series.
In this context the extension of holomorphic functions of a complex variable is developed as the holomorphic functional calculus.