Results 41 to 50 of about 19,971 (282)
Analogies between random matrix ensembles and the one-component plasma in two-dimensions
Nuclear Physics B, 2016 The eigenvalue PDF for some well known classes of non-Hermitian random matrices — the complex Ginibre ensemble for example — can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains.
Peter J. Forrester
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A New Real Structure-preserving Quaternion QR Algorithm
, 2017 New real structure-preserving decompositions are introduced to develop fast and robust algorithms for the (right) eigenproblem of general quaternion matrices.
Chen, Yong +3 more
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Quaternions and matrices of quaternions
Linear Algebra and its Applications, 1997 The author gives a useful survey on quaternions and matrices of quaternions. He recalls standard facts going back to Rowan Hamilton as well as new results motivated by applications in physical theories. The main research problem presented in the paper is to extend the classical matrix theory from complex to the quaternion matrices.
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, 2018 Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices.
Enshaeifar, Shirin +6 more
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Asymptotics of finite system Lyapunov exponents for some random matrix ensembles [PDF]
, 2015 For products $P_N$ of $N$ random matrices of size $d \times d$, there is a natural notion of finite $N$ Lyapunov exponents $\{\mu_i\}_{i=1}^d$. In the case of standard Gaussian random matrices with real, complex or real quaternion elements, and extended ...
Forrester, Peter J.
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On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem
MathematicsThe application of eigenvalue theory to dual quaternion Hermitian matrices holds significance in the realm of multi-agent formation control. In this paper, we study the use of Rayleigh quotient iteration (RQI) for solving the right eigenpairs of dual ...
Shan-Qi Duan +2 more
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Roth’s solvability criteria for the matrix equations AX - XB^ = C and X - AXB^ = C over the skew field of quaternions with aninvolutive automorphism q ¿ qˆ [PDF]
, 2016 The matrix equation AX-XB = C has a solution if and only if the matrices A C 0 B and A 0 0 B are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988)
Futorny, Vyacheslav +2 more
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Boundary Value Problems, 2023 This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential equations (QDEs).
Jie Liu, Siyu Sun, Zhibo Cheng
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FEBS Letters, EarlyView.Fluorescent probes allow dynamic visualization of phosphoinositides in living cells (left), whereas mass spectrometry provides high‐sensitivity, isomer‐resolved quantitation (right). Their synergistic use captures complementary aspects of lipid signaling. This review illustrates how these approaches reveal the spatiotemporal regulation and quantitative
Hiroaki Kajiho +3 more
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T-Eigenvalues of Third-Order Quaternion Tensors
MathematicsIn this paper, theories, algorithms and properties of eigenvalues of quaternion tensors via the t-product termed T-eigenvalues are explored. Firstly, we define the T-eigenvalue of quaternion tensors and provide an algorithm to compute the right T ...
Zhuo-Heng He, Mei-Ling Deng, Shao-Wen Yu
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