Split quaternion matrices

Alagöz, Yasemin; Oral, Khürsat Hakan; Yüce, Salîm

doi:10.18514/mmn.2012.364

Cited by 57 publications

(42 citation statements)

References 5 publications

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“…Recently in [8] the q-determinant of coquaternionic matrices has been introduced by the follows. Let A = A 1 + A 2 j ∈ H n×n , where A 1 and A 2 are complex matrices.…”

Section: Coquaternions Coquaternion Matrices and Noncommutative Detementioning

confidence: 99%

Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations

Kyrchei

2017

Adv. Appl. Clifford Algebras

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In this paper properties of the determinant of a Hermitian matrix are investigated, and determinantal representations of the inverse of a Hermitian coquaternionic matrix are given. By their using, Cramer's rules for left and right systems of linear equations with Hermitian coquaternionic matrices of coefficients are obtained. Cramer's rule for a two-sided coquaternionic matrix equation AXB = D (with Hermitian A, B) is given as well.

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“…Recently in [8] the q-determinant of coquaternionic matrices has been introduced by the follows. Let A = A 1 + A 2 j ∈ H n×n , where A 1 and A 2 are complex matrices.…”

Section: Coquaternions Coquaternion Matrices and Noncommutative Detementioning

confidence: 99%

Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations

Kyrchei

2017

Adv. Appl. Clifford Algebras

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“…Recently there was conducted a number of studies in split quaternion matrices (see, for ex. [11]- [14]). The matrix representation for the complex quaternions, which is also a split quaternion algebra, has been introduced in [15].…”

Section: Quaternion Algebramentioning

confidence: 99%

The Column and Row Immanants Over A Split Quaternion Algebra

Kyrchei

2015

Adv. Appl. Clifford Algebras

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The theory of the column-row determinants has been considered for matrices over a non-split quaternion algebra. In this paper the concepts of column-row determinants are extending to a split quaternion algebra. New definitions of the column and row immanants (permanents) for matrices over a non-split quaternion algebra are introduced, and their basic properties are investigated. The key theorem about the column and row immanants of a Hermitian matrix over a split quaternion algebra is proved. Based on this theorem an immanant of a Hermitian matrix over a split quaternion algebra is introduced.

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“…In [15] the authors also state an important result relating the degree of a coquaternionic polynomial with the maximum number of zeros that the polynomial may have. 1 The main purpose of this paper is to present a complete and simpler proof of the referred result on the maximum number of zeros of a coquaternionic polynomial and simultaneously to describe the zero-structure of such polynomials. A new result giving conditions which guarantee the existence of a special type of zeros -which we call linear zeros -is also presented and a positive answer to a question posed in [15] is given.…”

Section: Introductionmentioning

confidence: 99%

The number of zeros of unilateral polynomials over coquaternions revisited

Falcão

Miranda

Severino

et al. 2018

Linear and Multilinear Algebra

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The literature on quaternionic polynomials and, in particular, on methods for determining and classifying their zero-sets, is fast developing and reveals a growing interest on this subject. In contrast, polynomials defined over the algebra of coquaternions have received very little attention from researchers. One of the few exceptions is the very recent paper by Janovská and Opfer [Electronic Transactions on Numerical Analysis, Volume 46, pp. 55-70, 2017], where, among other results, we can find a first attempt to prove that a unilateral coquaternionic polynomial of degree n has, at most, n(2n − 1) zeros.In this paper we present a full proof of the referred result, using a totally different and, from our point of view, much simpler approach. Also, we give a complete characterization of the zero-sets of such polynomials and present a new result giving conditions which guarantee the existence of a special type of zeros. An algorithm to compute and classify all the zeros of a coquaternionic polynomial is proposed and several numerical examples are carefully constructed.

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Split quaternion matrices

Cited by 57 publications

References 5 publications

Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations

Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations

The Column and Row Immanants Over A Split Quaternion Algebra

The number of zeros of unilateral polynomials over coquaternions revisited

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