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 are nearly decomposable matrices we consider the problem of finding matrices each with exactly one nonzero entry so that

**[1]**D. Hartfiel,*On the structure of the certain matrix classes*, Dissertation, Univ. of Houston, Houston, Tex., 1969.**[2]**-,*A simplified form for nearly reducible and nearly decomposable matrices*, Proc. Amer. Math. Soc.**24**(1970), 388-393. MR**0252415 (40:5635)****[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 -matrices*, Proc. Amer. Math. Soc.**22**(1969), 117-123. MR**0245585 (39:6891)****[5]**Richard Sinkhorn,*Concerning a conjecture of Marshall Hall*, Proc. Amer. Math. Soc.**21**(1969), 192-201. MR**39**#2780. MR**0241440 (39:2780)****[6]**Richard Sinkhorn and Paul Knopp,*Problems involving diagonal products in nonnegative matrices*, Trans. Amer. Math. Soc.**136**(1969), 67-75. MR**0233830 (38:2151)**

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DOI:
https://doi.org/10.1090/S0002-9939-1971-0268062-4

Keywords:
-matrices,
construction,
canonical form

Article copyright:
© Copyright 1971
American Mathematical Society