Definitions for split-quaternion
split-quater·nion

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1. Split-quaternion

   In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers. After introduction in the 20th century of coordinate-free definitions of rings and algebras, it was proved that the algebra of split-quaternions is isomorphic to the ring of the 2×2 real matrices. So the study of split-quaternions can be reduced to the study of real matrices, and this may explain why there are few mentions of split-quaternions in the mathematical literature of the 20th and 21st centuries.

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1. Split-quaternion

   In abstract algebra, the split-quaternions or coquaternions are elements of a 4-dimensional associative algebra introduced by James Cockle in 1849 under the latter name. Like the quaternions introduced by Hamilton in 1843, they form a four dimensional real vector space equipped with a multiplicative operation. Unlike the quaternion algebra, the split-quaternions contain zero divisors, nilpotent elements, and nontrivial idempotents. As a mathematical structure, they form an algebra over the real numbers, which is isomorphic to the algebra of 2 × 2 real matrices. The coquaternions came to be called split-quaternions due to the division into positive and negative terms in the modulus function. For other names for split-quaternions see the Synonyms section below. The set {1, i, j, k} forms a basis. The products of these elements are²²² and hence ijk = 1. It follows from the defining relations that the set {1, i, j, k, −1, −i, −j, −k} is a group under coquaternion multiplication; it is isomorphic to the dihedral group of a square. A coquaternion has a conjugate and multiplicative modulus²²²² This quadratic form is split into positive and negative parts, in contrast to the positive definite form on the algebra of quaternions.

How to pronounce split-quaternion?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say split-quaternion in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of split-quaternion in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of split-quaternion in Pythagorean Numerology is: 3

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Split-Quaternion
2. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=split-quaternion