The Quaternion Numbers
نویسندگان
چکیده
منابع مشابه
The Quaternion Numbers
In this article, we define the set H of quaternion numbers as the set of all ordered sequences q = 〈x, y,w, z〉 where x,y,w and z are real numbers. The addition, difference and multiplication of the quaternion numbers are also defined. We define the real and imaginary parts of q and denote this by x = R(q), y = I1(q), w = I2(q), z = I3(q). We define the addition, difference, multiplication again...
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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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In this article, we give some equality and basic theorems about quaternion numbers, and some special operations. the notation and terminology for this paper. In this paper z 1 , z 2 , z 3 , z 4 , z are quaternion numbers. The following propositions are true: (1) (z 1 · z 2) = (z 2 · z 1). (2) If z is a real number, then z + z 3 = (z) + (z 3) + 1 (z 3) · i + 2 (z 3) · j + 3 (z 3) · k. (4) If z i...
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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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In previous paper [1] an approach to nonlinear dynamical modeling of interaction between automatic (A) and conscious (C) processes in the brain was presented. The idea is to use complex field with real and imaginary components representing Aand C-processes. The interaction is due to the nonlinearity of the system. This approach was illustrated on the nonlinear equation for the current density i...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2006
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-006-0020-1