<s>
In	O
statistics	O
,	O
the	O
matrix	B-General_Concept
variate	I-General_Concept
beta	I-General_Concept
distribution	I-General_Concept
is	O
a	O
generalization	O
of	O
the	O
beta	O
distribution	O
.	O
</s>
<s>
If	O
is	O
a	O
positive	B-Algorithm
definite	I-Algorithm
matrix	I-Algorithm
with	O
a	O
matrix	B-General_Concept
variate	I-General_Concept
beta	I-General_Concept
distribution	I-General_Concept
,	O
and	O
are	O
real	O
parameters	O
,	O
we	O
write	O
(	O
sometimes	O
)	O
.	O
</s>
<s>
If	O
is	O
any	O
constant	O
,	O
matrix	O
of	O
rank	O
,	O
then	O
has	O
a	O
generalized	O
matrix	B-General_Concept
variate	I-General_Concept
beta	I-General_Concept
distribution	I-General_Concept
,	O
specifically	O
.	O
</s>
<s>
Mitra	O
proves	O
the	O
following	O
theorem	O
which	O
illustrates	O
a	O
useful	O
property	O
of	O
the	O
matrix	B-General_Concept
variate	I-General_Concept
beta	I-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
Assume	O
that	O
is	O
positive	B-Algorithm
definite	I-Algorithm
and	O
that	O
.	O
</s>
<s>
where	O
,	O
then	O
has	O
a	O
matrix	B-General_Concept
variate	I-General_Concept
beta	I-General_Concept
distribution	I-General_Concept
.	O
</s>
