On linear transformations preserving at least one eigenvalue |
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| Authors: | S Akbari M Aryapoor |
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| Institution: | Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran ; Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran |
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| Abstract: | Let  be an algebraically closed field and  be a linear transformation. In this paper we show that if  preserves at least one eigenvalue of each matrix, then  preserves all eigenvalues of each matrix. Moreover, for any infinite field  (not necessarily algebraically closed) we prove that if  is a linear transformation and for any  with at least an eigenvalue in  ,  and  have at least one common eigenvalue in  , then  preserves the characteristic polynomial. |
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| Keywords: | Linear transformation preserve eigenvalue |
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