Conjugacy classes; Jordan Normal Form
1
Compute the conjugacy classes of the following groups:
GL3(C);GL3(Z2);GL4 (R)
I mean, do I have to use the Jordan Normal Form?
abstract-algebra
asked Dec 9 '18 at 21:32
Mike Hawk
61
add a comment |
1
Compute the conjugacy classes of the following groups:
GL3(C);GL3(Z2);GL4 (R)
I mean, do I have to use the Jordan Normal Form?
abstract-algebra
asked Dec 9 '18 at 21:32
Mike Hawk
61
Yes, that is the right idea. Just be careful with those fields that are not algebraically closed. Of course, it is not clear what kind of answer you are looking for, so maybe you can step out to the algebraic closure... But I guess you should describe them using matrices in the given rings, so once again, be careful with the last two.
– A. Pongrácz
Dec 9 '18 at 21:40
1
You don’t have to... but in general any kind of canonical form will make your life easier. Note that you cannot use the Jordan canonical form over $mathbb{R}$ or over $mathbb{Z}_2$, but you can use the rational canonical form.
– Arturo Magidin
Dec 9 '18 at 22:24
add a comment |
1
1
1
Compute the conjugacy classes of the following groups:
GL3(C);GL3(Z2);GL4 (R)
I mean, do I have to use the Jordan Normal Form?
abstract-algebra
asked Dec 9 '18 at 21:32
Mike Hawk
61
Compute the conjugacy classes of the following groups:
GL3(C);GL3(Z2);GL4 (R)
I mean, do I have to use the Jordan Normal Form?
abstract-algebra
abstract-algebra
asked Dec 9 '18 at 21:32
Mike Hawk
61
asked Dec 9 '18 at 21:32
Mike Hawk
61
asked Dec 9 '18 at 21:32
Mike Hawk
61
asked Dec 9 '18 at 21:32
Mike Hawk
61
asked Dec 9 '18 at 21:32
Mike Hawk
61
61
Yes, that is the right idea. Just be careful with those fields that are not algebraically closed. Of course, it is not clear what kind of answer you are looking for, so maybe you can step out to the algebraic closure... But I guess you should describe them using matrices in the given rings, so once again, be careful with the last two.
– A. Pongrácz
Dec 9 '18 at 21:40
1
You don’t have to... but in general any kind of canonical form will make your life easier. Note that you cannot use the Jordan canonical form over $mathbb{R}$ or over $mathbb{Z}_2$, but you can use the rational canonical form.
– Arturo Magidin
Dec 9 '18 at 22:24
add a comment |
Yes, that is the right idea. Just be careful with those fields that are not algebraically closed. Of course, it is not clear what kind of answer you are looking for, so maybe you can step out to the algebraic closure... But I guess you should describe them using matrices in the given rings, so once again, be careful with the last two.
– A. Pongrácz
Dec 9 '18 at 21:40
1
You don’t have to... but in general any kind of canonical form will make your life easier. Note that you cannot use the Jordan canonical form over $mathbb{R}$ or over $mathbb{Z}_2$, but you can use the rational canonical form.
– Arturo Magidin
Dec 9 '18 at 22:24
Yes, that is the right idea. Just be careful with those fields that are not algebraically closed. Of course, it is not clear what kind of answer you are looking for, so maybe you can step out to the algebraic closure... But I guess you should describe them using matrices in the given rings, so once again, be careful with the last two.
– A. Pongrácz
Dec 9 '18 at 21:40
Yes, that is the right idea. Just be careful with those fields that are not algebraically closed. Of course, it is not clear what kind of answer you are looking for, so maybe you can step out to the algebraic closure... But I guess you should describe them using matrices in the given rings, so once again, be careful with the last two.
– A. Pongrácz
Dec 9 '18 at 21:40
1
1
You don’t have to... but in general any kind of canonical form will make your life easier. Note that you cannot use the Jordan canonical form over $mathbb{R}$ or over $mathbb{Z}_2$, but you can use the rational canonical form.
– Arturo Magidin
Dec 9 '18 at 22:24
You don’t have to... but in general any kind of canonical form will make your life easier. Note that you cannot use the Jordan canonical form over $mathbb{R}$ or over $mathbb{Z}_2$, but you can use the rational canonical form.
– Arturo Magidin
Dec 9 '18 at 22:24
add a comment |
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Yes, that is the right idea. Just be careful with those fields that are not algebraically closed. Of course, it is not clear what kind of answer you are looking for, so maybe you can step out to the algebraic closure... But I guess you should describe them using matrices in the given rings, so once again, be careful with the last two.
– A. Pongrácz
Dec 9 '18 at 21:40
1
You don’t have to... but in general any kind of canonical form will make your life easier. Note that you cannot use the Jordan canonical form over $mathbb{R}$ or over $mathbb{Z}_2$, but you can use the rational canonical form.
– Arturo Magidin
Dec 9 '18 at 22:24