四元数矩阵,">左特征值,">二次数值域, 四元数矩阵,">左特征值,">二次数值域, quaternion matrix, left eigenvalues,quadratic numerical range,"/> <span style="font-size: 10.5pt;">Quadratic numerical range of a quaternion matrix</span>

SHANDONG SCIENCE ›› 2016, Vol. 29 ›› Issue (3): 87-91.doi: 10.3976/j.issn.1002-4026.2016.03.015

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Quadratic numerical range of a quaternion matrix

GUO Yi-wan, ZHAI Fa-hui   

  1. Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China
  • Received:2015-08-07 Online:2016-06-20 Published:2016-06-20

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Abstract:

We present the definition of quadratic numerical range of a quaternion matrix, and discuss its properties. We further prove that the set of all left eigenvalues of such a matrix is its subset under certain restricted conditions. These results are benefit for the research on the left eigenvalues of a quaternion matrix and relative issues.

Key words: quaternion matrix')">quaternion matrix, left eigenvalues, quadratic numerical range

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  • Cite this article

    GUO Yi-wan, ZHAI Fa-hui. Quadratic numerical range of a quaternion matrix[J].SHANDONG SCIENCE, 2016, 29(3): 87-91.

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