Results 11 to 20 of about 77,287 (351)
Quaternion Electromagnetism and the Relation with Two-Spinor Formalism
Universe, 2019 By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely.
In Ki Hong, Choong Sun Kim
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Field Equations in the Complex Quaternion Spaces [PDF]
Advances in Mathematical Physics, 2014 The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents of two fields,
Zi-Hua Weng
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Angular momentum and torque described with the complex octonion
AIP Advances, 2014 The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields.
Zi-Hua Weng
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Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
Special Matrices, 2014 L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331(2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformationsA ↦ ˜S−1AS in which S is a nonsingular quaternion matrix ...
Klimchuk Tatiana, Sergeichuk Vladimir V.
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Nature, 1893 PROF. MACFARLANE claims that his “fundamental rules for vectors are based on physical considerations, the principal one of which is that the square of a vector is essentially positive.” His proof is virtually this:—The expression for the kinetic energy (½ mv2) is an essentially positive quantity. It contains one factor ½m evidently positive.
A. Lodge
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On the arithmetic of quaternions [PDF]
Transactions of the American Mathematical Society, 1940 Gordon Pall
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The Discussion on Quaternions [PDF]
Nature, 1893 I HAVE followed with much interest the discussion on quaternions which has with more or less intermission been going on in NATURE for a long time.
Robert S. Ball
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A quaternionic Nullstellensatz [PDF]
Journal of Pure and Applied Algebra, 2021 We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the quaternions, and more generally, over any division algebra.
Elad Paran, Gil Alon
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Communications in Mathematical Physics, 1996 We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for holomorphic pairs.
Okonek, Christian, Teleman, Andrei
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