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15.2.2  Jordan normal form

The egvl or eigenvalues or eigVl command finds the Jordan form of a matrix.

Examples

egvl([[4,1,-2],[1,2,-1],[2,1,0]])
     
⎡
⎢
⎢
⎣
210
021
002
⎤
⎥
⎥
⎦
          
egvl([[4,1,0],[1,2,-1],[2,1,0]])
     
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
    
rootof⎛
⎝		⎡
⎣		⎡
⎣		1,0,−20,0,100⎤
⎦		,⎡
⎣		1,0,−24,0,144,0,−148⎤
⎦		⎤
⎦		⎞
⎠
18
00
    0
rootof⎛
⎝		⎡
⎣		⎡
⎣		−1,0,20,18,8⎤
⎦		,⎡
⎣		1,0,−24,0,144,0,−148⎤
⎦		⎤
⎦		⎞
⎠
36
0
    00
rootof⎛
⎝		⎡
⎣		⎡
⎣		−1,0,20,−18,8⎤
⎦		,⎡
⎣		1,0,−24,0,144,0,−148⎤
⎦		⎤
⎦		⎞
⎠
36
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
          

See Section 11.1.21 for a discussion of rootof.

evalf(egvl([[4,1,0],[1,2,-1],[2,1,0]]))
     
⎡
⎢
⎢
⎣
1.460811127190.00.0
0.04.214319743380.0
0.00.00.324869129433
⎤
⎥
⎥
⎦
          
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