Definition:Hurwitz Quaternion

Definition

A Hurwitz quaternion is a quaternion whose components are all either:

integers

or:

integers plus a half, that is, halves of odd integers.

The set $H$ of all Hurwitz quaternions can therefore be defined as:

$H = \set {a + b \mathbf i + c \mathbf j + d \mathbf k \in \H: \paren {a, b, c, d \in \Z} \text { or } \paren {a, b, c, d \in \Z + \dfrac 1 2} }$

Also see

• Definition:Lipschitz Quaternion

Source of Name

This entry was named for Adolf Hurwitz.

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