On the Cardinalities of the Row spaces of Non-full Rank Boolean Matrices
Tóm tắt
-2 integers 2
n
-2+2
n
-3+2
s
, where s=0,1,2,...,n-3, in the interval (2
n
-2+2
n
-3,2
n
-1] such that these integers are the cardinalities of row spaces R(A) of non-full rank Boolean matrices A of order n. We also show that for each s, where s=0,1,2,...,n-3, there exists A epsilon B
n
such that A is non-full rank and the cardinality of R(A) equals 2
n
-2+2
n
-3+2
s
.