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quaternion    
n. 四个一组,四人一组,四元数

四个一组,四人一组,四元数

quaternion
四元数

quaternion
n 1: the cardinal number that is the sum of three and one [synonym:
{four}, {4}, {IV}, {tetrad}, {quatern}, {quaternion},
{quaternary}, {quaternity}, {quartet}, {quadruplet},
{foursome}, {Little Joe}]

Quaternion \Qua*ter"ni*on\, v. t.
To divide into quaternions, files, or companies. --Milton.
[1913 Webster]


Quaternion \Qua*ter"ni*on\, n. [L. quaternio, fr. quaterni four
each. See {Quaternary}.]
1. The number four. [Poetic]
[1913 Webster]

2. A set of four parts, things, or person; four things taken
collectively; a group of four words, phrases,
circumstances, facts, or the like.
[1913 Webster]

Delivered him to four quaternions of soldiers.
--Acts xii. 4.
[1913 Webster]

Ye elements, the eldest birth
Of Nature's womb, that in quaternion run. --Milton.
[1913 Webster]

The triads and quaternions with which he loaded his
sentences. -- Sir W.
Scott.
[1913 Webster]

3. A word of four syllables; a quadrisyllable.
[1913 Webster]

4. (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.
[1913 Webster]

Note: The science or calculus of quaternions is a new
mathematical method, in which the conception of a
quaternion is unfolded and symbolically expressed, and
is applied to various classes of algebraical,
geometrical, and physical questions, so as to discover
theorems, and to arrive at the solution of problems.
--Sir W. R. Hamilton.
[1913 Webster]


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  • Quaternion - Wikipedia
    In mathematics, the quaternion number system extends the complex numbers Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 [1][2] and applied to mechanics in three-dimensional space
  • Quaternion -- from Wolfram MathWorld
    The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton
  • _TZ_32678-magnolia-cs-iastate-edu. dvi
    Quaternions are very efficient for analyzing situations where rotations in R3 are involved A quaternion is a 4-tuple, which is a more concise representation than a rotation matrix Its geo-metric meaning is also more obvious as the rotation axis and angle can be trivially recovered
  • Introducing The Quaternions - Department of Mathematics
    Take any unit imaginary quaternion, u = u1i + u2j + u3k That is, any unit vector
  • 1. 2: Quaternions - Mathematics LibreTexts
    The quaternions, discovered by William Rowan Hamilton in 1843, were invented to capture the algebra of rotations of 3-dimensional real space, extending the way that the complex numbers capture the algebra of rotations of 2-dimensional real space
  • Quaternions: What Are They, and Do We Really Need Them?
    A quaternion contains four components and it is expressed in the form: a+bi+cj+dk, where a, b, c, and d are real numbers, while i, j, and k are unconventional imaginary units (or the quaternion units)
  • QUATERNION Definition Meaning - Merriam-Webster
    The meaning of QUATERNION is a set of four parts, things, or persons
  • Quaternion | Rotations, Hypercomplex Numbers, Algebra | Britannica
    quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions Quaternions and rules for operations on them were invented by Irish mathematician Sir William Rowan Hamilton in 1843 He devised them as a way of describing three-dimensional problems in mechanics
  • Quaternion - Encyclopedia of Mathematics
    Quaternions were historically the first example of a hypercomplex system, arising from attempts to find a generalization of complex numbers Complex numbers are depicted geometrically by points in the plane and operations on them correspond to the simplest geometric transformations of the plane
  • Rotation Quaternions, and How to Use Them - DancesWithCode
    We give a simple definition of quaternions, and show how to convert back and forth between quaternions, axis-angle representations, Euler angles, and rotation matrices We also show how to rotate objects forward and back using quaternions, and how to concatenate several rotation operations into a single quaternion





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