Results 11 to 20 of about 9,570 (204)
The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra
SymmetryIn this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB = C, and present the general solution expression when the solvability conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by ...
Kai-Wen Si, Qing-Wen Wang
openaire +3 more sources
Quaternion Convolutional Neural Networks for End-to-End Automatic Speech Recognition [PDF]
, 2018 Recently, the connectionist temporal classification (CTC) model coupled with recurrent (RNN) or convolutional neural networks (CNN), made it easier to train speech recognition systems in an end-to-end fashion.
Bengio, Yoshua +6 more
core +3 more sources
Quaternionic representation of the genetic code [PDF]
, 2015 A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin ...
Carlevaro, C. Manuel +2 more
core +3 more sources
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
core +2 more sources
On the Eigenvalues and Eigenvectors of a Lorentzian Rotation Matrix by Using Split Quaternions
Advances in Applied Clifford Algebras, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Özdemir, Mustafa +2 more
openaire +3 more sources
Time-Reversal Symmetry in Non-Hermitian Systems
, 2011 For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1.
Berry +4 more
core +1 more source
A Clifford algebra associated to generalized Fibonacci quaternions
, 2014 In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice ...
Flaut, Cristina
core +1 more source
, 2014 In this paper, the consimilarity of complex matrices is generalized for the split quaternions. In this regard, coneigenvalue and coneigenvector are defined for split quaternion matrices. Also, the existence of solution to the split quaternion matrix equation X-AXB = C is characterized and the solution of the equation in the explicit form are derived ...
Kosal, Hidayet Huda +2 more
openaire +2 more sources
Electronics Letters, 2014 In most algorithms that use quaternion numbers, the key operation is a quaternion multiplication, of which the efficiency and accuracy obviously determine the same properties of the whole computational scheme of a filter or transform.
Petrovsky, N. +2 more
openaire +1 more source