Quaternionic eigenvalue problem
TL;DR: In this paper, the eigenvalue equation for linear quaternionic operators is discussed, and the possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternion problem into an {\em equivalent} real or complex counterpart.
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Abstract: We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.
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Citations
Quaternion-MUSIC for vector-sensor array processing
TL;DR: A MUSIC-like algorithm is presented, allowing estimation of wave's DOAs and polarization parameters, and it results in a reduction by half of memory requirements for representation of data covariance model and reduces the computational effort, for equivalent performance.
A new structure-preserving method for quaternion Hermitian eigenvalue problems
TL;DR: The algorithm is based on the structure-preserving tridiagonalization of the real counterpart for quaternion Hermitian matrices by applying orthogonal JRS-symplectic matrices and is very efficient, it costs about a quarter arithmetical operations, and a quarter to one-eighth CPU times, comparing with standard general-purpose algorithms.
95
Edge detection of colour image based on quaternion fractional differential
TL;DR: In this paper, the authors extended the real fractional differential (RDF) to quaternion body and put forward a new concept: quaternions fractional differentiation (QFD), and applied it to edge detection of colour image.
78
Geršgorin type theorems for quaternionic matrices
Fuzhen Zhang,Fuzhen Zhang +1 more
TL;DR: In this paper, the authors present the Gersgorin type theorems for the left and right eigenvalues of square quaternionic matrices, and conclude the paper with examples showing and summarizing some differences between complex matrices and quaternion matrices.
74
Split quaternion matrices
TL;DR: In this article, a complex adjoint matrix of split quaternion matrices is defined and the definition of q-determinant is given for the q-decomposition matrix of a split quadratic matrix.
70
References
Quaternions and matrices of quaternions
TL;DR: A brief survey on quaternions and matrices of quaternion is given in this article, where the authors present new proofs for certain known results and discuss the quaternionic analogues of complex matrices.
1.1K
•Book
Matrices ' Methods and Applications'
Stephen Barnett
- 21 Jun 1990
TL;DR: In this article, a basic algebra of matrices is defined, including unique solution of linear equations, determinant and inverse rank, non-unique solution of equations, and applications.
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