What's the difference between quaternion and vector?
Quaternion
Definition:
(n.) The number four.
(n.) A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
(n.) A word of four syllables; a quadrisyllable.
(n.) The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
(v. t.) To divide into quaternions, files, or companies.
Example Sentences:
(1) During visually guided movements, arm follows gaze, and the nine-dimensional rotatory configuration space for eye-head-arm-synergies (three degrees of freedom for each system) is reduced to a two-dimensional plane in the space of quaternion vectors.
(2) Many testable predictions made by quaternion models also turn up in models based on other mathematics.
(3) Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion.
(4) The four-component rotational operators called quaternions, which represent eye rotations in terms of their axes and angles, have several advantages over other representations of eye position (such as Fick coordinates): they provide easy computations, symmetry, a simple form for Listing's law, and useful three-dimensional plots of eye movements.
(5) In other words, angular eye positions in space (expressed as quaternions) were constrained to a two-dimensional surface.
(6) Findings 1 and 3 show that saccadic control signals accurately reflect the properties of three-dimensional rotations, as predicted by a new quaternion model of the saccadic system; models that approximate rotational kinematics using vectorial addition and integration do not predict these findings.
(7) Tweed and Vilis (Journal of Neurophysiology, 58, 832-849, 1987) have argued that quaternion algebra provides the most appropriate description of the rotations of the eye, and have derived a three-dimensional model of gaze control based on quaternion operations.
(8) A canonical unitary representation of the Euclidean group on the range space of the Gabor transform is constructed from mathematical properties of the Euclidean group and the quaternions.
(9) The positions of the arm in space were described by quaternion vectors, i.e., a particular position was described in terms of the axis and amplitude of a rotation from a reference position to that position.
(10) In this paper we present algorithms for computing eye position quaternions and eye angular velocity (not the derivative of position in three dimensions) from two search coils (not necessarily orthogonal) on one eye in two or three magnetic fields, and for locating primary position using quaternions.
(11) In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions.
Vector
Definition:
(n.) Same as Radius vector.
(n.) A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
Example Sentences:
(1) The dependence of fluorescence polarization of stained nerve fibres on the angle between the fibre axis and electrical vector of exciting light (azimuth characteristics) has been considered.
(2) A beta-adrenergic receptor cDNA cloned into a eukaryotic expression vector reliably induces high levels of beta-adrenergic receptor expression in 2-12% of COS cell colonies transfected with this plasmid after experimental conditions are optimized.
(3) We have constructed retroviral vectors derived from the genome of avian erythroblastosis virus ES4 (AEV ES4).
(4) The 6.6-kb DNA Bam HI fragment containing the resistance gene was cloned with the plasmid vector pIJ699.
(5) The plasmid pMucAMucB, constructed from the Haemophilus influenzae vector pDM2, and a similar plasmid, constructed from pBR322, increased the survival after UV irradiation of Escherichia coli AB1157 with the umu-36 mutation and also caused UV-induced mutation in the E. coli strain.
(6) In assessing damaged nets and curtains it must be recognised that anything less than the best vector control may have no appreciable impact on holoendemic malaria.
(7) When an expression vector containing plasminogen cDNA is transfected into baby hamster kidney cells, the number of drug-resistant colonies as well as the levels of plasminogen secreted by those colonies is lower than observed in similar transfections of other protease precursor genes.
(8) The vector is relatively small (6 kilobase pairs) and contains a portion of the L. seymouri alpha-tubulin gene positioned in-frame with a truncated neomycin phosphotransferase gene that confers resistance to the aminoglycoside G418.
(9) The presence of potential insect vectors and the occurrence of clinical signs are indications of active transmissions.
(10) Subcloning of pLR beta 118 into a transcription vector with subsequent in vitro transcription and translation using the reticulocyte lysate system in the presence of microsomes followed by immunoprecipitation with mAb OX6 and two-dimensional gel electrophoresis revealed the intact RT1.B beta I-chain.
(11) It is the most commonly reported vector-borne disease in the United States, where the incidence is highest in the eastern and midwestern states.
(12) The primary focus of the government at this point is vector control,” said Nadal.
(13) Transfer of the shuttle vectors from B. uniformis donors to E. coli occurred at the same frequencies when the matings were done aerobically or anaerobically.
(14) Discovery of this vectorhost-parasite system in the Americas, and the localization of promastigote flagellates (leptomonads) in the hindgut of the vector, should assist in clarifying interpretative problems associated with infection of wild-caught flies in studies on leishmaniasis in the Americas and elsewhere.
(15) ELISA, cDNA dot blot hybridization and transmission by vector aphids were used to investigate the occurrence and degree of cross-protection produced in oat plants by virus isolates representing five strains or serotypes of barley yellow dwarf virus, namely PAV, MAV, SGV, RPV and RMV.
(16) The results suggests that abrin B chain of chimeric protein may act as a vector to carry ACTI into the tumor cells.
(17) The peak biting activity of the vector and peak appearance of microfilariae in the peripheral blood occurred at about 01.00 h, which accounts for the optimum infection of the vector population.
(18) The transposon-containing plasmids were used to localize essential replication functions and to characterize the stability of large inserts in these vectors.
(19) A recombinant gene encoding human growth hormone (hGH) was stably introduced into cultured myoblasts with a retroviral vector.
(20) While it has been possible to readily produce large numbers of such templates from M13 or other single-stranded vectors for several years, the sequencing of double-stranded DNA templates using the ABI 373 DNA Sequencer has had a considerably lower success rate.