Civil Engineering Reference
In-Depth Information
a
00 0
0 0 0
00 0
11
a
22
[]
=
A
a
33
000
a
nn
2.2.4
IDENTITY MATRIX
An
identity matrix
is a diagonal matrix where all of the elements along the
principal diagonal are equal to one and is denoted [
I
].
100
0
010
0
[]
=
001
0
000 1
2.2.5
TRIANGULAR MATRIX
When all of the elements on one side of the principal diagonal are zero,
this matrix is a
triangular matrix
. There are two types of triangular
matrices, upper and lower. An
upper triangular matrix
, [
U
], is when all of
the elements below the principal diagonal are zero, and a
lower triangular
matrix
, [
L
], occurs when all of the elements above the principal diagonal
are zero.
aaa a
aa a
a
11
12
13
1
n
0
00
22
23
2
n
[]
=
U
a
33
3
n
000
a
nn
a
aa
aaa
00 0
0
11
0
0
21
22
[]
=
L
31
32
33
aaa
a
n
1
n
2
n
3
nn
