Jordan form of the matrices of a group
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Let's consider a set of $m$ generic square matricies $(N;N) $ defined on $R$ which forms a group. Chosen one of these $ m $ matrices, I know that, by changing the base on my vectorial space, I can obtain a diagonal matrix or at least a matrix in a Jordan form. My question is, does exist a particular change of basis rapresented by the matrix $T$, which diagonalizes or puts in Jordan form all the matrices of the group? If so, how is this matrix $T$?
linear-algebra jordan-normal-form
asked Nov 24 at 16:54
Landau
447
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up vote
1
down vote
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Let's consider a set of $m$ generic square matricies $(N;N) $ defined on $R$ which forms a group. Chosen one of these $ m $ matrices, I know that, by changing the base on my vectorial space, I can obtain a diagonal matrix or at least a matrix in a Jordan form. My question is, does exist a particular change of basis rapresented by the matrix $T$, which diagonalizes or puts in Jordan form all the matrices of the group? If so, how is this matrix $T$?
linear-algebra jordan-normal-form
asked Nov 24 at 16:54
Landau
447
I think at least the group should be Abelian.
– xbh
Nov 24 at 16:57
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let's consider a set of $m$ generic square matricies $(N;N) $ defined on $R$ which forms a group. Chosen one of these $ m $ matrices, I know that, by changing the base on my vectorial space, I can obtain a diagonal matrix or at least a matrix in a Jordan form. My question is, does exist a particular change of basis rapresented by the matrix $T$, which diagonalizes or puts in Jordan form all the matrices of the group? If so, how is this matrix $T$?
linear-algebra jordan-normal-form
asked Nov 24 at 16:54
Landau
447
Let's consider a set of $m$ generic square matricies $(N;N) $ defined on $R$ which forms a group. Chosen one of these $ m $ matrices, I know that, by changing the base on my vectorial space, I can obtain a diagonal matrix or at least a matrix in a Jordan form. My question is, does exist a particular change of basis rapresented by the matrix $T$, which diagonalizes or puts in Jordan form all the matrices of the group? If so, how is this matrix $T$?
linear-algebra jordan-normal-form
linear-algebra jordan-normal-form
asked Nov 24 at 16:54
Landau
447
asked Nov 24 at 16:54
Landau
447
asked Nov 24 at 16:54
Landau
447
asked Nov 24 at 16:54
Landau
447
asked Nov 24 at 16:54
Landau
447
447
I think at least the group should be Abelian.
– xbh
Nov 24 at 16:57
add a comment |
I think at least the group should be Abelian.
– xbh
Nov 24 at 16:57
I think at least the group should be Abelian.
– xbh
Nov 24 at 16:57
I think at least the group should be Abelian.
– xbh
Nov 24 at 16:57
add a comment |
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I think at least the group should be Abelian.
– xbh
Nov 24 at 16:57