# quaternion

## Definitions

• WordNet 3.6
• n quaternion the cardinal number that is the sum of three and one
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Webster's Revised Unabridged Dictionary
• Quaternion A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like. "Delivered him to four quaternions of soldiers.""Ye elements, the eldest birth Of Nature's womb, that in quaternion run.""The triads and quaternions with which he loaded his sentences."
• Quaternion A word of four syllables; a quadrisyllable.
• Quaternion The number four.
• Quaternion (Math) 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 Quaternion To divide into quaternions, files, or companies.
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Century Dictionary and Cyclopedia
• n quaternion A set, group, or body of four: applied to persons or things.
• n quaternion A word of four syllables; a quadrisyllable.
• n quaternion A fourfold quantity capable of being expressed in the form xi + yj + zk + w, where x, y, z, w are scalars, or real numbers, while i, j, k are vectors, or quantities whose squares are negative scalars. The calculus of such quantities is termed quaternions.
• quaternion To divide into quaternions, files, or companies.
• n quaternion In book-making, a set or ‘gathering’ of four sheets of paper or parchment folded in two.
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Chambers's Twentieth Century Dictionary
• n Quaternion a set or group of four: a word of four syllables:
• n Quaternion (pl.) in mathematics, a calculus of peculiar power and generality invented by Sir W. R. Hamilton of Dublin, as a geometry, primarily concerning itself with the operations by which one directed quantity or vector is changed into another
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## Etymology

Webster's Revised Unabridged Dictionary
L. quaternio, fr. quaterni, four each. See Quaternary

## Usage

### In literature:

It was ten years after the discovery that the great volume appeared under the title of "Lectures on Quaternions," Dublin, 1853.
"Great Astronomers" by R. S. Ball
Last month I delivered a lecture on Quaternions.
"A Mortal Antipathy" by Oliver Wendell Holmes, Sr.
We do not fulminate against a treatise on Quaternions because it lacks humor.
"The Dramatic Values in Plautus" by Wilton Wallace Blancke
All knowledge is good; from the theory of quaternions to the way to cut a ham-frill.
"Septimus" by William J. Locke
Index Moralium omnium, & eorum quae in ipsis tractantur, habetur in hoc quaternione.
"Catalogue of the William Loring Andrews Collection of Early Books in the Library of Yale University" by Anonymous
La Place, and all the great mathematicians of that period, had scarcely passed away when the more powerful Quaternion system began to dawn.
"Personal Recollections, from Early Life to Old Age, of Mary Somerville" by Mary Somerville
The other great contribution made by Hamilton to mathematical science, the invention of Quaternions, is treated under that heading.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 8" by Various
As regard class (1) of the first quaternion, like Sancho Panza I have no intention of indicating how old these may be.
"Legends & Romances of Spain" by Lewis Spence
Four soldiers formed a quaternion; four quaternions therefore were sixteen men, who were especially appointed to guard Peter.
""Granny's Chapters"" by Lady Mary Ross
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### In science:

Ginibre, Statistical ensembles of complex, quaternion and real matrices, J.
Determinantal random point fields
W are real (or self-dual) quaternions for all gauge ﬁelds.
Random Matrix Theory and Chiral Symmetry in QCD
These are implemented by choosing the matrix elements of W to be real, complex, or quaternion real for β = 1, β = 2, and β = 4, respectively.
Random Matrix Theory and Chiral Symmetry in QCD
In this case, the quaternion real matrix elements of W satisfy the reality relation W ∗k l = σ2Wk lσ2 .
Random Matrix Theory and Chiral Symmetry in QCD
In this case, if the system is invariant under time reversal, the elements of H are quaternion real.
Random Matrix Theory and Chiral Symmetry in QCD
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