Chemistry Reference
In-Depth Information
2.3 SPECIAL MATRICES
1. The null matrix (even rectangular, all elements are zero):
0
@
1
A
00
0
00
0
0 ¼
ð
2
12
Þ
:
00
0
0þA ¼ Aþ0 ¼AA
0
¼ 0A ¼
0
ð
same order
Þ
ð
2
13
Þ
:
2. The diagonal matrix (order n):
0
@
1
A
l
1
0
0
0
l
0
2
L
¼
l
ij
¼
l
i
d
ij
ð
2
14
Þ
:
00
l
n
d
ij
is the Kronecker delta.
3. The identity matrix (order n):
where
0
@
1
A
10
0
01
0
1
¼
1
ij
¼ d
ij
ð
2
15
Þ
:
00
1
1
A ¼ A
1
¼ A ð
same order
Þ
ð
2
16
Þ
:
4. The scalar matrix (order n):
0
@
1
A
l
0
0
0
l
0
L
¼
¼
l
1
ð
2
17
Þ
:
00
l
