I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2008, VOLUME 14, NUMBER 4, PAGES 231-268
Matrices with different Gondran--Minoux and determinantal ranks over
Ya. N. Shitov
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the row Gondran--Minoux rank of a matrix, be the column
Gondran--Minoux rank, and be the determinantal
The following problem was posed by M. Akian, S. Gaubert, and
A. Guterman: Find the minimal numbers and such that there exists an
-matrix with different row and
column Gondran--Minoux ranks.
We prove that in the case the minimal and are equal to and , respectively, and in the
case the numbers and are minimal.
An example of a matrix such that
It is proved that and are the minimal numbers
such that there exists an -matrix with
different row Gondran--Minoux and determinantal ranks.
Last modified: February 27, 2009