Abstract
The main purpose of this paper is to set a method of finding eigenvalues of split quaternion matrices. In particular, we will give an extension of Gershgorin theorem, which is one of the fundamental theorems of complex matrix theory, for split quaternion matrices.
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Alagöz Y., Oral K. H., Yüce S.: Split Quaternion Matrices. Miskolc Mathematical Notes 13, 223–232 (2012)
Baker A.: Right eigenvalues for quaternionic matrices: A topological approach. Linear Algebra and its Applications 286, 303–309 (1999)
Farid F. O.: Topics on a Generalization of Gershgorin’s Theorem. Linear Algebra and its Applications 268, 91–116 (1998)
Farid F.O., Wang Q.W., Zhang F.: On the eigenvalues of quaternion matrices. Linear and Multilinear Algebra 59, 451–473 (2011)
Huang L., Huang L.: On left eigenvalues of a quaternionic matrix. Linear Algebra and its Applications 323, 105–116 (2001)
Kula L., Yayh Y.: Split Quaternions and Rotations in Semi Euclidean Space. Journal of Korean Mathematical Society 44, 1313–1327 (2007)
Özdemir M., Ergin A.A.: Rotations with unit timelike quaternions in Minkowski 3-space. Journal of Geometry and Physics 56, 322–336 (2006)
Özdemir M.: Roots of a Split Quaternion. Applied Mathematics Letters 22, 258–263 (2009)
Zhang F.: Quaternions and Matrices of Quaternions. Linear Algebra and its Applications 251, 21–57 (1997)
Zhang F.: Gershgorin type theorems for quaternionic matrices. Linear Algebra and its Applications 424, 139–153 (2007)
Zhou B., Lam J., Duan G. R.: Toward solution of matrix equation X = Af(X)B + C. Linear Algebra and Its Applications 435, 1370–1398 (2011)
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Erdoğdu, M., Özdemir, M. On Eigenvalues of Split Quaternion Matrices. Adv. Appl. Clifford Algebras 23, 615–623 (2013). https://doi.org/10.1007/s00006-013-0391-7
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DOI: https://doi.org/10.1007/s00006-013-0391-7