Abstract
Let s 1, ..., s n be arbitrary complex scalars. It is required to construct an n × n normal matrix A such that s i is an eigenvalue of the leading principal submatrix A i , i = 1, 2, ..., n. It is shown that, along with the obvious diagonal solution diag(s 1, ..., s n ), this problem always admits a much more interesting nondiagonal solution A. As a rule, this solution is a dense matrix; with the diagonal solution, it shares the property that each submatrix A i is itself a normal matrix, which implies interesting connections between the spectra of the neighboring submatrices A i and A i + 1.
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M. Arav, D. Hershkowitz, V. Mehrmann, and H. Schneider, “The Recursive Inverse Eigenvalue Problem,” SIAM J. Matrix Anal. Appl. 22, 392–412 (2000).
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Original Russian Text © Kh.D. Ikramov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 5, pp. 771–775.
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Ikramov, K.D. On a recursive inverse eigenvalue problem. Comput. Math. and Math. Phys. 49, 743–747 (2009). https://doi.org/10.1134/S0965542509050017
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DOI: https://doi.org/10.1134/S0965542509050017