Category:Quaternion Modulus

This category contains results about the Quaternion Modulus.

Definition 1

The (quaternion) modulus of $\mathbf x$ is the real-valued function defined and denoted as:

$\size {\mathbf x} := \sqrt {a^2 + b^2 + c^2 + d^2}$

Definition 2

Let $\mathbf x$ be expressed in matrix form:

$\mathbf x = \begin {bmatrix} a + b i & c + d i \\ -c + d i & a - b i \end {bmatrix}$

The (quaternion) modulus of $\mathbf x$ is the real-valued function defined and denoted as:

$\size {\mathbf x} := \sqrt {\map \det {\mathbf x} }$