Definition:Quaternion/Mistake

Source Work

 * Chapter $1$: Introductory Concepts
 * $1$. Basic Building Blocks
 * $1$. Basic Building Blocks

Mistake

 * Every quaternion can be represented in the form
 * $q = q_0 1 + q_1 \lambda_1 + q_2 \lambda_2 + q_3 \lambda_3$
 * where the $q_i \, \paren {i = 0, 1, 2, 3}$ are real numbers and the $\lambda_1$ have multiplicative properties defined by

Correction
The representation of $q$ should read:


 * $q = q_0 \lambda_0 + q_1 \lambda_1 + q_2 \lambda_2 + q_3 \lambda_3$

and the line:
 * $\lambda_i \lambda_i = -\lambda_0$

holds only for $i = 1, 2, 3$ because:
 * $\lambda_0 \lambda_0 = \lambda_0$

One suspects that the author conflated this presentation with one where $\lambda_0$ has been identified with the number $1$, and only partially has this been translated into its current form.