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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 - Stanford University
    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
  • 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
  • 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
  • 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
  • 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)
  • 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 why do we need to know?
    ions provide ‘the’ way to represent rotations Why? Unit quaternions allow a clear visualization (see Hanson, 2006) of the space of rotations as the unit sphere S in four dimensions (with antipodal points identified) Unit quaternions make it possible to dif
  • Don’t Get Lost in Deep Space: Understanding Quaternions
    Quaternions are mathematical operators that are used to rotate and stretch vectors This article provides an overview to aid in understanding the need for quaternions in applications like space navigation Accurately locating, shifting, and rotating objects in space can be done in a variety of ways





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