Results 51 to 60 of about 77,287 (351)
Quaternion Approach to the Measurement of the Local Birefringence Distribution in Optical Fibers
IEEE Photonics Journal, 2015 A method to structure the Jones quaternion utilizing Pauli matrices is proposed, improving the quaternion theory of polarization optics. It is proved that the Stokes quaternion is the double product of the Jones quaternion and its Hermitian transpose and
Lanlan Liu +4 more
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Generalised quadratic forms and the u-invariant [PDF]
, 2017 The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and
Dolphin, Andrew
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Quaternions and matrices of quaternions
Linear Algebra and its Applications, 1997 AbstractWe give a brief survey on quaternions and matrices of quaternions, present new proofs for certain known results, and discuss the quaternionic analogues of complex matrices. The methods of converting a quaternion matrix to a pair of complex matrices and homotopy theory are emphasized.
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“The Elements of Quaternions” [PDF]
Nature, 1894 IN answer to my reviewer's question (vide p. 154), I must frankly admit that (a) Eq. 8, p. 40, should have been a group of six equations, , , c and that (b) The inference should have been that i, j, &c, are (unequal) square roots of negative unity.
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On Fibonacci Quaternions [PDF]
Advances in Applied Clifford Algebras, 2011 In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions. Moreover, we derive some sums formulas for them.
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Differentiable functions of quaternion variables [PDF]
, 2002 We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions.
Ludkovsky, S. V., van Oystaeyen, F.
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Enabling quaternion derivatives: the generalized HR calculus [PDF]
Royal Society Open Science, 2015 Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective
Dongpo Xu +3 more
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Quaternions: A Mathematica Package for Quaternionic Analysis [PDF]
, 2011 This paper describes new issues of theMathematica standard package Quaternions for implementing Hamilton's Quaternion Algebra. This work attempts to endow the original package with the ability to perform operations on symbolic expressions involving quaternion-valued functions.
Falcão, M. I., Miranda, Fernando
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Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion
Mathematics, 2023 The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing.
Jiang-Feng Chen +3 more
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