When is possible to use an orthogonal matrix to put in Jordan form a matrix?
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I know that if I have a symmetrical matrix defined on $R$, it is always diagonalisable and I can always find beetwen the matrix of its eigenspaces an orthogonal matrix. While if I have a non diagonalisable matrix, of course I can put it in Jordan normal form, however how the matrix must be to be able to find out an orthogonal matrix of its generalized eigenvectors?
linear-algebra jordan-normal-form
asked Dec 4 '18 at 13:43
LandauLandau
447
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add a comment |
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I know that if I have a symmetrical matrix defined on $R$, it is always diagonalisable and I can always find beetwen the matrix of its eigenspaces an orthogonal matrix. While if I have a non diagonalisable matrix, of course I can put it in Jordan normal form, however how the matrix must be to be able to find out an orthogonal matrix of its generalized eigenvectors?
linear-algebra jordan-normal-form
asked Dec 4 '18 at 13:43
LandauLandau
447
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I'm not aware of any nice criteria in this direction unless the Jordan normal form is diagonal.
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 20:27
add a comment |
$begingroup$
I know that if I have a symmetrical matrix defined on $R$, it is always diagonalisable and I can always find beetwen the matrix of its eigenspaces an orthogonal matrix. While if I have a non diagonalisable matrix, of course I can put it in Jordan normal form, however how the matrix must be to be able to find out an orthogonal matrix of its generalized eigenvectors?
linear-algebra jordan-normal-form
asked Dec 4 '18 at 13:43
LandauLandau
447
$endgroup$
I know that if I have a symmetrical matrix defined on $R$, it is always diagonalisable and I can always find beetwen the matrix of its eigenspaces an orthogonal matrix. While if I have a non diagonalisable matrix, of course I can put it in Jordan normal form, however how the matrix must be to be able to find out an orthogonal matrix of its generalized eigenvectors?
linear-algebra jordan-normal-form
linear-algebra jordan-normal-form
asked Dec 4 '18 at 13:43
LandauLandau
447
asked Dec 4 '18 at 13:43
LandauLandau
447
edited Dec 4 '18 at 14:09
Landau
asked Dec 4 '18 at 13:43
LandauLandau
447
asked Dec 4 '18 at 13:43
LandauLandau
447
asked Dec 4 '18 at 13:43
LandauLandau
447
447
$begingroup$
I'm not aware of any nice criteria in this direction unless the Jordan normal form is diagonal.
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 20:27
add a comment |
$begingroup$
I'm not aware of any nice criteria in this direction unless the Jordan normal form is diagonal.
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 20:27
$begingroup$
I'm not aware of any nice criteria in this direction unless the Jordan normal form is diagonal.
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 20:27
$begingroup$
I'm not aware of any nice criteria in this direction unless the Jordan normal form is diagonal.
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 20:27
add a comment |
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$begingroup$
I'm not aware of any nice criteria in this direction unless the Jordan normal form is diagonal.
$endgroup$
– Qiaochu Yuan
Dec 4 '18 at 20:27