Mathematical Notes

, Volume 60, Issue 6, pp 649–657 | Cite as

Normal dilatation of triangular matrices

  • Kh. D. Ikramov


LetR be a (real or complex) triangular matrix of ordern, say, an upper triangular matrix. Is it true that there exists a normaln×n matrixA whose upper triangle coincides with the upper triangle ofR? The answer to this question is “yes” and is obvious in the following cases: (1)R is real; (2)R is a complex matrix with a real or a pure imaginary main diagonal, and moreover, all the diagonal entries ofR belong to a straight line. The answer is also in the affirmative (although it is not so obvious) for any matrixR of order 2. However, even forn=3 this problem remains unsolved. In this paper it is shown that the answer is in the affirmative also for 3×3 matrices.

Key words

triangular matrix normal matrix upper triangular matrix 


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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Kh. D. Ikramov
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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