Universal Journal of Mathematics and Mathematical Sciences
Volumes 7, Issue 2, Pages 121 - 131
(April 2015) http://dx.doi.org/10.17654/UJMMSApr2015_121_131 |
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THE CLOSURE OF QUATERNION MATRIX’S SIMILARITY ORBIT
Yiwan Guo and Fahui Zhai
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Abstract: Let A be a quaternion matrix, be the standard eigenvalues of A, be the minimal polynomial of A. The quaternion similarity orbit of the quaternion matrix A is defined as the set is any invertible quaternion matrix}. In this paper, we show that the norm closure of is the set is the quaternion matrix: for all where denotes the rank of quaternion matrix T, is a monic polynomial with real coefficients, denotes dividing |
Keywords and phrases: quaternion matrix, quaternion similarity orbit, minimal polynomial, rank. |
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