Paper Abstract and Keywords |
Presentation |
2023-10-11 15:35
A Complex Vector-Scalar Ring theory Osamu Ichiyoshi (HNfB21C) SAT2023-57 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The quaternion is an expansion of complex number to three dimensions of imaginary numbers. It is a useful tool in calculating rotation of vectors around a given axis in the three dimensional space. The imaginary numbers in quaternion can be replaced with real vectors in the three-dimensional space to give a Vector-Scalar (VS). The set of whole vector-scalars is algebraically equivalent to that of quaternions; they form rings. The transition is made by a definition of vector-scalar product (x) as follows. For vectors u and v, u (x) v = u x v – (u.v), where u x v and (u.v) are respectively normal vector product and scalar product. For any vector l with unit length, l (x) l = -1, which is similar to the imaginary number i. In fact the following formula e^(lθ) = cos(θ) + l.sin(θ) can be defined just as Euler’s formula in complex number theory. The coefficients in VS can take complex values to achieve a fundamental unification of vector-scalars and complex numbers. Functions in VS domain can be defined in much the same manners as in complex plane enabling to solve wide ranges of vectors and scalars problems. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
vector / scalar / vector-scalar / vector-scalar product / rotation / axis / coordinate conversion / quaternion |
Reference Info. |
IEICE Tech. Rep., vol. 123, no. 204, SAT2023-57, pp. 50-55, Oct. 2023. |
Paper # |
SAT2023-57 |
Date of Issue |
2023-10-03 (SAT) |
ISSN |
Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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SAT2023-57 |
Conference Information |
Committee |
SAT KOSST |
Conference Date |
2023-10-10 - 2023-10-11 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Central Hotel Marianne(Korea, Busan) |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
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Paper Information |
Registration To |
SAT |
Conference Code |
2023-10-SAT-KOSST |
Language |
English (Japanese title is available) |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
A Complex Vector-Scalar Ring theory |
Sub Title (in English) |
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vector |
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scalar |
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vector-scalar |
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vector-scalar product |
Keyword(5) |
rotation |
Keyword(6) |
axis |
Keyword(7) |
coordinate conversion |
Keyword(8) |
quaternion |
1st Author's Name |
Osamu Ichiyoshi |
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Human Network for Better 21 Century (HNfB21C) |
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Speaker |
Author-1 |
Date Time |
2023-10-11 15:35:00 |
Presentation Time |
25 minutes |
Registration for |
SAT |
Paper # |
SAT2023-57 |
Volume (vol) |
vol.123 |
Number (no) |
no.204 |
Page |
pp.50-55 |
#Pages |
6 |
Date of Issue |
2023-10-03 (SAT) |
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