Hypercomplex numbers

matrices important in quantum mechanics and the study of spin

element of a unital algebra over the field of real numbers

element of the real commutative associative algebra ℝ[j] / (j² − 1), i.e. the reals with an extra square root of +1 adjoined

algebra over a field

manner in which higher-dimension algebras may be produced

commutative, associative algebra of two complex dimensions

anticommutating number

theorem on finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form