  Using elementary linear algebra, this paper clarifies and proves some
concepts about a recently introduced octonion-like associative division algebra
over R. This octonion-like algebra is actually the same as the
split-biquaternion algebra, an even subalgebra of Clifford algebra Cl(4,0). For
two seminorms described in the paper, it is shown that the octonion-like
algebra is a seminormed composition algebra over R. Moreover, additional
results related to the computation of inverse numbers in the octonion-like
algebra are introduced, showing that the octonion-like algebra is a seminormed
division algebra over R, i.e., division by any number is possible as long as
the two seminorms are non-zero. Additional results on normalization of
octonion-like numbers and some involutions are also presented. The elementary
linear algebra descriptions used in the paper also allow straightforward
software implementations of the octonion-like algebra.
