There are at least two definitions of hypercomplex numbers. Clifford algebraists call their higher dimensional numbers hypercomplex, even though they do not share all the properties of complex numbers and no classical function theory can be constructed over them. According to van der Waerden, a hypercomplex number is a number having properties departing from those of the real and complex numbers. The most common examples are biquaternions, exterior algebras, group algebras, matrices, octonions, and quaternions.

biquaternion | Cayley number | Clifford algebra | complex number | exterior algebra | group | matrix | octonion | quaternion | real number | Weierstrass's theorem