5.48.2 Eigenvalues:
egvl
eigenvalues
eigVl
The
egvl
command finds the Jordan form of a matrix.
eigenvalues
and
eigVl
are synonyms for
egvl
.
egvl
takes one argument:
A
, a square matrix.
egvl(
A
)
returns the Jordan normal form of
A
.
Examples
Input:
egvl([[4,1,-2],[1,2,-1],[2,1,0]])
Output:
⎡
⎢
⎢
⎣
2
1
0
0
2
1
0
0
2
⎤
⎥
⎥
⎦
Input:
egvl([[4,1,0],[1,2,-1],[2,1,0]])
Output:
See Section
5.27.21
for a discussion of
rootof
.
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
rootof
⎛
⎝
⎡
⎣
⎡
⎣
1,0,−20,0,100
⎤
⎦
,
⎡
⎣
1,0,−24,0,144,0,−148
⎤
⎦
⎤
⎦
⎞
⎠
18
0
0
0
rootof
⎛
⎝
⎡
⎣
⎡
⎣
−1,0,20,18,8
⎤
⎦
,
⎡
⎣
1,0,−24,0,144,0,−148
⎤
⎦
⎤
⎦
⎞
⎠
36
0
0
0
rootof
⎛
⎝
⎡
⎣
⎡
⎣
−1,0,20,−18,8
⎤
⎦
,
⎡
⎣
1,0,−24,0,144,0,−148
⎤
⎦
⎤
⎦
⎞
⎠
36
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Input:
evalf(egvl([[4,1,0],[1,2,-1],[2,1,0]]))
Output:
⎡
⎢
⎢
⎣
1.46081112719
0.0
0.0
0.0
4.21431974338
0.0
0.0
0.0
0.324869129433
⎤
⎥
⎥
⎦