  The general linear quaternion function of degree one is a sum of terms with
quaternion coefficients on the left and right. The paper considers the canonic
form of such a function, and builds on the recent work of Todd Ell, who has
shown that any such function may be represented using at most four quaternion
coefficients. In this paper, a new and simple method is presented for obtaining
these coefficients numerically using a matrix approach which also gives an
alternative proof of the canonic forms.
