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Matrices with a sequence of accretive powers

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Abstract

It is shown that a matrix satisfying a certain spectral condition which has an infinite sequence of accretive powers is unitarily similar to the direct sum of a normal matrix and a nilpotent matrix. If the sequence of exponents is forcing or semiforcing then the spectral condition is automatically satisfied. If, further, the index of 0 as an eigenvalue ofA is at most 1 or the first term of the sequence of exponents is 1, then the matrix is positive semidefinite or positive definite. There are applications to matrices with a sequence of powers that areM-matrices.

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Authors and Affiliations

  1. Mathematics Department, University of Wisconsin, 53706, Madison, WI, USA

    Danieŀ Hershkowitz & Hans Schneider

  2. Department of Mathematics, Technion — Israel Institute of Technology, 32000, Haifa, Israel

    Danieŀ Hershkowitz & Hans Schneider

Authors
  1. Danieŀ Hershkowitz
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  2. Hans Schneider
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Additional information

The research of the second author was supported in part by NSF grant DMS-8320189, by ONR grant N00014-85-K-1613 and by the Lady Davis Foundation of Israel.

The first author is located permanently at the Technion and the second author at the University of Wisconsin.

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Hershkowitz, D., Schneider, H. Matrices with a sequence of accretive powers. Israel J. Math. 55, 327–344 (1986). https://doi.org/10.1007/BF02765030

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  • DOI: https://doi.org/10.1007/BF02765030

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