Definition:Octonion/Addition

Definition

Let $x = \tuple {a, b}$ and $y = \tuple {c, d}$ be octonions, where $a, b, c, d \in \H$ are quaternions.

The sum of $x$ and $y$ is defined as:

$x + y = \tuple {a, b} + \tuple {c, d} = \tuple {a + c, b + d}$