Right eigenvalues for quaternionic matrices: A topological approach

Baker, Andrew

doi:10.1016/s0024-3795(98)10181-7

Cited by 52 publications

(48 citation statements)

References 2 publications

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“…Then det F n D P n .x/; x 2 R and F n is strictly row diagonally dominant if and only if jxj > 4 3 . It is shown (Theorem 6.02, [16]), that when n 2 and for jxj > 4 …”

Section: Diagonal Dominancementioning

confidence: 99%

Infinite Matrices and Their Recent Applications

Shivakumar¹,

Sivakumar²,

Zhang³

2016

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“…Then det F n D P n .x/; x 2 R and F n is strictly row diagonally dominant if and only if jxj > 4 3 . It is shown (Theorem 6.02, [16]), that when n 2 and for jxj > 4 …”

Section: Diagonal Dominancementioning

confidence: 99%

Infinite Matrices and Their Recent Applications

Shivakumar¹,

Sivakumar²,

Zhang³

2016

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“…Right eigenvalues have been studied extensively (see, for example, [1,4,15]). We will work with right eigenvalues towards our main result.…”

Section: Definitions and Basic Propertiesmentioning

confidence: 99%

The Moore–Penrose inverses of matrices over quaternion polynomial rings

Huang

Wang

Zhang

2015

Linear Algebra and its Applications

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MSC: 15A09 68W30Keywords: Quaternion polynomial matrix Moore-Penrose inverse Leverrier-Faddeev algorithm In this paper, we define and discuss the Moore-Penrose inverses of matrices with quaternion polynomial entries. When the Moore-Penrose inverses exist, we prove that LeverrierFaddeev algorithm works for these matrices by using generalized characteristic polynomials. Furthermore, after studying interpolations for quaternion polynomials, we give an efficient algorithm to compute the Moore-Penrose inverses. We developed a Maple package for quaternion polynomial matrices. All algorithms in this paper are implemented, and tested on examples.

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“…There are many studies on matrices of the real quaternions. So, Baker discussed right eigenvalues of the real quaternion matrices with a topological approach in [2]. On the other hand, Huang and So introduced on left eigenvalues of the real quaternion matrices [10].…”

Section: Introductionmentioning

confidence: 99%

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Kösal

Akyiğit

Tosun

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In this regard, we examine the solvability conditions and general solutions of the equations a x = xb and A X = XB in split quaternions and split quaternion matrices, respectively. Moreover, coneigenvalue and coneigenvector are defined for split quaternion matrices. Some consequences are also presented.

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Right eigenvalues for quaternionic matrices: A topological approach

Cited by 52 publications

References 2 publications

Infinite Matrices and Their Recent Applications

Infinite Matrices and Their Recent Applications

The Moore–Penrose inverses of matrices over quaternion polynomial rings

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

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