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On constructing nearly decomposable matrices


Author: D. J. Hartfiel
Journal: Proc. Amer. Math. Soc. 27 (1971), 222-228
MSC: Primary 05.25; Secondary 15.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0268062-4
MathSciNet review: 0268062
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Abstract: In this paper we consider the construction of nearly decomposable matrices from nearly decomposable matrices of smaller dimension. In particular, if $ {A_1},{A_2}, \cdots ,{A_s}$ are nearly decomposable matrices we consider the problem of finding matrices $ {E_1},{E_2}, \cdots ,{E_s}$ each with exactly one nonzero entry so that

$\displaystyle \left[ {\begin{array}{*{20}{c}}{{A_1}} & 0 & { \cdots 0} & {{E_1}... ...& \cdots & \cdots \\ 0 & 0 & { \cdots {E_s}} & {{A_s}} \\ \end{array} } \right]$

is nearly decomposable.

References [Enhancements On Off] (What's this?)

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  • [3] M. Marcus and H. Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, Mass., 1964. MR 29 #112. MR 0162808 (29:112)
  • [4] Henryk Minc, On lower bounds for permanents of $ (0,1)$-matrices, Proc. Amer. Math. Soc. 22 (1969), 117-123. MR 0245585 (39:6891)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0268062-4
Keywords: $ (0,1)$-matrices, construction, canonical form
Article copyright: © Copyright 1971 American Mathematical Society

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