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where
c
t
u
,v
w
=
a
k
i
,
l
j
◦
b
p
r
,
q
s
,
for
t
u
=
k
i
=
p
r
∈
K
∩
P
and
v
w
=
l
j
=
q
s
∈
L
∩
Q
.
The geometrical interpretation of ope
ration
⊗
(
◦
)
is
Multiplication
A
(
◦
,
∗
)
B
=[
K
∪
(
P
−
L
),
Q
∪
(
L
−
P
),
{
c
t
u
,v
w
}]
,
where
⎧
⎨
a
k
i
,
l
j
,
if
t
u
=
k
i
∈
K
and
v
w
=
l
j
∈
L
−
P
−
Q
b
p
r
,
q
s
,
if
t
u
=
∈
−
−
v
w
=
q
s
∈
p
r
P
L
K
and
Q
c
t
u
,v
w
=
◦
⎩
a
k
i
,
l
j
∗
b
p
r
,
q
s
,
if
t
u
=
k
i
∈
K
and
v
w
=
q
s
∈
Q
l
j
=
p
r
∈
L
∩
P
0
,
otherwise
is substituted by
j
j
Obviously, when
◦
is substituted by
+
, the symbol
.
The geometrical interpretation of the multiplication between two ordinary matri-
ces is illustrated as follows,
while the geometrical interpretation of the multiplication between two IMs is
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