JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 2, Pages 161 - 179
(August 2002)
|
|
SIGN
PATTERNS THAT REQUIRE ALL DISTINCT EIGENVALUES
Zhongshan Li (USA) and Laura Harris (USA)
|
Abstract: An
n ´ n sign pattern
matrix A requires all distinct eigenvalues if
every real matrix whose sign pattern is represented
by A has n distinct eigenvalues. In
this paper, a number of sufficient and/or necessary
conditions for a sign pattern to require all
distinct eigenvalues are established. Further, for n
= 2 and 3, the n ´ n sign
patterns that require all distinct eigenvalues are
determined. |
Keywords and phrases: sign pattern matrices,
distinct eigenvalues, cycles, permutational
similarity, signature similarity, discriminant. |
|
Number of Downloads: 14 | Number of Views: 1157 |
|