Bounds for Eigenvalues of Matrix Polynomials Over Quaternion Division Algebra

Ahmad, Sk. Safique; Ali, Istkhar

doi:10.1007/s00006-016-0640-7

Cited by 7 publications

(2 citation statements)

References 25 publications

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“…In fact, they are useful when one only needs approximate values or starting values for algorithms. As can be seen in [1] and references therein, where left and right eigenvalues of quaternionic matrices were considered, the aspects of location and bounds have received attention in the quaternionic context.…”

Section: Introductionmentioning

confidence: 99%

Bounds for the zeros of unilateral octonionic polynomials

Serôdio

Beites

Vitória

2021

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.

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Section: Introductionmentioning

confidence: 99%

Bounds for the zeros of unilateral octonionic polynomials

Serôdio

Beites

Vitória

2021

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…Also in [22], the general partitioned linear representation form of matrix quaternions are obtained. Localization theorems are discussed for the left and right eigenvalues of block quaternion matrices in [23]. In [24], some sufficient conditions for two, three and four quaternion matrices are block independent in the least squares inverse, the minimum norm inverse and the 1,3,4-inverse are derived respectively.…”

Section: Introductionmentioning

confidence: 99%

Some New Properties of The Real Quaternion Matrices and Matlab Applications

Nalbant

Yüce

2019

Cumhuriyet Science Journal

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In this study, firstly, it was shown that the set of real quaternion matrices   MH n is a 4dimensional module over the real matrix ring   M n and 2-dimensional module over the complex matrix ring   M n. Moreover, some new properties of the real quaternion matrices were described. Then, matrix representations of the real quaternion matrices were found easily by Matlab. These matrices were also applied to find the inverse of the real quaternion matrices and inverse matrices were obtained easily with these matrices. In addition, some new properties for matrix representations of the real quaternion matrices were found. Also, the inverse of the 22  real quaternion block matrices was obtained by new methods. Finally, a new method to calculate the determinant of the 22  real quaternion matrices was found and the determinant of these matrices was calculated easily with Matlab application.

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