Definition:Quaternion Modulus/Definition 1

Definition
Let $\mathbf x = a \mathbf 1 + b \mathbf i + c \mathbf j + d \mathbf k$ be a quaternion, where $a, b, c, d \in \R$.

The (quaternion) modulus of $\mathbf x$ is the real-valued function defined and denoted as:
 * $\size {\mathbf x} := \sqrt {a^2 + b^2 + c^2 + d^2}$

Also see

 * Equivalence of Definitions of Quaternion Modulus