Databases Reference
In-Depth Information
Thus, it is expected that the number of matrices with 0 determinant vi-
brates between 4(
N
+1) and (
N
+1)(
N
+ 2). The variance will become larger
when
N
grows. In other words, the probability of
det
= 0 will vibrate between
O
(1
/N
2
)and
(1
/N
). The variance will become larger when
N
grows.
It is notable that the above discussion can be applied to a general case,
such as
ad
O
bc
=
k
, or other constraint. For example, if we have a constraint
such as
a/
(
a
+
b
)or
a/
(
a
+
c
), then we can analyze a constraint for accuracy
or coverage. It will be our future work to investigate such cases.
−
6 Empirical Validations
For empirical validations, we calculate the whole combination of a 2
×
2 matrix
with fixed sample size (0
≤
N
≤
100)
M
(2
,
2
,N
).
6.1 Total Number of
M
(2
,
2
,N
)
Figure 1 plots the relation between sample size
N
and the total number of
M
(2
,
2
,N
). This figure clearly shows that the relation is polynomial.
On the other hand, Fig. 2, which plots the relation between sample size
and the total number of matrices with zero determinant, gives an interesting
feature. As discussed in Sect. 5, the total number vibrates and the amplitude
180000
Total Number of Matrices with N samples
160000
140000
120000
100000
80000
60000
40000
20000
0
0
20
40
60
80
100
# of Samples (N)
Fig. 1.
Total number of
M
(2
,
2
,N
)
