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On linear transformations preserving at least one eigenvalue

Akbari, S ; Sharif University of Technology | 2004

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  1. Type of Document: Article
  2. DOI: 10.1090/S0002-9939-03-07262-9
  3. Publisher: 2004
  4. Abstract:
  5. Let F be an algebraically closed field and T: Mn(F) → Mn(F) be a linear transformation. In this paper we show that if T preserves at least one eigenvalue of each matrix, then T preserves all eigenvalues of each matrix. Moreover, for any infinite field F (not necessarily algebraically closed) we prove that if T: Mn(F) → M n(F) is a linear transformation and for any A ∈ Mn(F) with at least an eigenvalue in F, A and T(A) have at least one common eigenvalue in F, then T preserves the characteristic polynomial
  6. Keywords:
  7. Eigenvalue ; Linear transformation ; Preserve
  8. Source: Proceedings of the American Mathematical Society ; Volume 132, Issue 6 , 2004 , Pages 1621-1625 ; 00029939 (ISSN)
  9. URL: https://www.ams.org/journals/proc/2004-132-06/S0002-9939-03-07262-9/S0002-9939-03-07262-9.pdf