Canonic form of linear quaternion functions
نویسنده
چکیده
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.
منابع مشابه
On Systems of Linear Quaternion Functions
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under functional composition. Furthermore, the composition operation is symbolically identical to quaternion multiplication, making manipulation and reduction of sy...
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