Inner Products, Group, Ring of Quaternion Numbers
نویسندگان
چکیده
منابع مشابه
Inner Products, Group, Ring of Quaternion Numbers
The articles [9], [1], [3], [4], [6], [5], [2], [7], and [8] provide the notation and terminology for this paper. We use the following convention: q, r, c, c1, c2, c3 are quaternion numbers and x1, x2, x3, x4, y1, y2, y3, y4 are elements of R. 0H is an element of H. 1H is an element of H. Next we state several propositions: (1) For all real numbers x, y, z, w holds 〈x, y, z, w〉H = x+y · i+ z · ...
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(1) <(z1 · z2) = <(z2 · z1). (2) If z is a real number, then z + z3 = <(z) + <(z3) + =1(z3) · i+ =2(z3) · j + =3(z3) · k. (3) If z is a real number, then z − z3 = 〈<(z)−<(z3),−=1(z3),−=2(z3), −=3(z3)〉H. (4) If z is a real number, then z · z3 = 〈<(z) · <(z3),<(z) · =1(z3),<(z) · =2(z3),<(z) · =3(z3)〉H. (5) If z is a real number, then z · i = 〈0,<(z), 0, 0〉H. (6) If z is a real number, then z · j...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2008
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-008-0019-x