# Matrices with a sequence of accretive powers

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DOI: 10.1007/BF02765030

- Cite this article as:
- Hershkowitz, D. & Schneider, H. Israel J. Math. (1986) 55: 327. doi:10.1007/BF02765030

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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 of*A* 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 are*M*-matrices.

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© Hebrew University 1986