منابع مشابه
On bilinear algorithms for multiplication in quaternion algebras
We show that the bilinear complexity of multiplication in a non-split quaternion algebra over a field of characteristic distinct from 2 is 8. This question is motivated by the problem of characterising algebras of almost minimal rank studied in [1] This paper is a translation of a report submitted by the author to the XI international seminar ”Discrete mathematics and its applications”. Definit...
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Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to exchanging formulas or implementations: there are two quaternion multiplications in common use, Hamilton’s multiplication and its flipped version, which is often...
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Protein side chain interactions between residues separated by at least one loop or turn or break in the amino acid sequence are called 'nonlocal contacts' in this manuscript, and contiguous sets of such interactions located between segments of secondary structure are called 'contact zones.' A new interactive program, the quaternion contact ribbon tool, has been developed to help protein chemist...
متن کاملQuaternion Involutions
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such involutions, and we show that the quaternions have an infinite number of involutions. We show that the conjugate of a quaternion may be expressed using three mu...
متن کاملDual Quaternion
As we know, quaternions are very efficient for representing rotations with clear geometric meaning (rotation axis and angle) and only one redundancy. Unfortunately, they do not handle translations, which meanwhile can be made multiplicative along with rotations via the use of homogeneous coordinates. Despite also being 4-tuples, homogeneous coordinates are algebraically incompatible with quater...
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ژورنال
عنوان ژورنال: IEEE Access
سال: 2017
ISSN: 2169-3536
DOI: 10.1109/access.2017.2705196