Message Boards

WOLFRAM COMMUNITY

1858 Views

2 Replies

1 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Mathematics Algebra Wolfram Language

Calculate generalized eigenvector using Jordan normal form.

Hongyi Zhao

Posted 1 year ago

I try to reproduce the example 5 given here: In[173]:= (Example 5) mA={{-14,2,-2,0},{4,0,2,0},{-3,0,0,1},{1,0,0,0}} mA//JordanDecomposition//RootReduce Out[173]= {{-14, 2, -2, 0}, {4, 0, 2, 0}, {-3, 0, 0, 1}, {1, 0, 0, 0}} Out[174]= {{{Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 1, 0], Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 2, 0], Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 3, 0], Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 4, 0]}, {Root[ 462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 2, 0], Root[ 462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 1, 0], Root[ 462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 3, 0], Root[ 462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 4, 0]}, {Root[ 29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 1, 0], Root[ 29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 2, 0], Root[ 29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 4, 0], Root[ 29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 3, 0]}, {1, 1, 1, 1}}, {{Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 1, 0], 0, 0, 0}, {0, Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 2, 0], 0, 0}, {0, 0, Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 3, 0], 0}, {0, 0, 0, Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 4, 0]}}} As shown above, I got a very complicated result and couldn't get the simple form given in the Wiki. Any tips for solving this problem? Regards, Zhao

I try to reproduce the example 5 given here:

enter image description here

In[173]:= (*Example 5*)
mA={{-14,2,-2,0},{4,0,2,0},{-3,0,0,1},{1,0,0,0}}
mA//JordanDecomposition//RootReduce

Out[173]= {{-14, 2, -2, 0}, {4, 0, 2, 0}, {-3, 0, 0, 1}, {1, 0, 0, 0}}

Out[174]= {{{Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 1, 0], 
   Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 2, 0], 
   Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 3, 0], 
   Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 4, 0]}, {Root[
   462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 2, 0], Root[
   462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 1, 0], Root[
   462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 3, 0], Root[
   462 - 274 # + 48 #^2 - 11 #^3 + 2 #^4& , 4, 0]}, {Root[
   29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 1, 0], Root[
   29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 2, 0], Root[
   29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 4, 0], Root[
   29 + 124 # + 104 #^2 + 34 #^3 + 4 #^4& , 3, 0]}, {1, 1, 1, 
   1}}, {{Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 1, 0], 0, 0, 
   0}, {0, Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 2, 0], 0, 0}, {0,
    0, Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 3, 0], 0}, {0, 0, 0, 
   Root[-4 + 14 # - 14 #^2 + 14 #^3 + #^4& , 4, 0]}}}

As shown above, I got a very complicated result and couldn't get the simple form given in the Wiki. Any tips for solving this problem?

Regards,
Zhao

POSTED BY: Hongyi Zhao