relation between minimal polynomial and jordan normal form
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I just solved some exercises on minimal polynomials and i remember that there is a relation between the minimal polynomial and the jordan normal form.
But my question is the following : knowing the minimal polynomial of a given matrix $A$ what information can we get about the jordan normal form (without computing it).
Thanks in advance!
linear-algebra matrices jordan-normal-form
edited Dec 10 '13 at 23:31
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asked Aug 12 '13 at 15:50
sigmatau
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up vote
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down vote
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I just solved some exercises on minimal polynomials and i remember that there is a relation between the minimal polynomial and the jordan normal form.
But my question is the following : knowing the minimal polynomial of a given matrix $A$ what information can we get about the jordan normal form (without computing it).
Thanks in advance!
linear-algebra matrices jordan-normal-form
edited Dec 10 '13 at 23:31
Git Gud
28.5k104898
asked Aug 12 '13 at 15:50
sigmatau
1,9751923
math.stackexchange.com/questions/82607/… has some information. I'm not sure there's much more you can do.
– Evan
Aug 12 '13 at 16:08
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I just solved some exercises on minimal polynomials and i remember that there is a relation between the minimal polynomial and the jordan normal form.
But my question is the following : knowing the minimal polynomial of a given matrix $A$ what information can we get about the jordan normal form (without computing it).
Thanks in advance!
linear-algebra matrices jordan-normal-form
edited Dec 10 '13 at 23:31
Git Gud
28.5k104898
asked Aug 12 '13 at 15:50
sigmatau
1,9751923
I just solved some exercises on minimal polynomials and i remember that there is a relation between the minimal polynomial and the jordan normal form.
But my question is the following : knowing the minimal polynomial of a given matrix $A$ what information can we get about the jordan normal form (without computing it).
Thanks in advance!
linear-algebra matrices jordan-normal-form
edited Dec 10 '13 at 23:31
Git Gud
28.5k104898
asked Aug 12 '13 at 15:50
sigmatau
1,9751923
edited Dec 10 '13 at 23:31
Git Gud
28.5k104898
edited Dec 10 '13 at 23:31
Git Gud
28.5k104898
edited Dec 10 '13 at 23:31
Git Gud
28.5k104898
28.5k104898
asked Aug 12 '13 at 15:50
sigmatau
1,9751923
asked Aug 12 '13 at 15:50
sigmatau
1,9751923
asked Aug 12 '13 at 15:50
sigmatau
1,9751923
1,9751923
math.stackexchange.com/questions/82607/… has some information. I'm not sure there's much more you can do.
– Evan
Aug 12 '13 at 16:08
add a comment |Â
math.stackexchange.com/questions/82607/… has some information. I'm not sure there's much more you can do.
– Evan
Aug 12 '13 at 16:08
math.stackexchange.com/questions/82607/… has some information. I'm not sure there's much more you can do.
– Evan
Aug 12 '13 at 16:08
math.stackexchange.com/questions/82607/… has some information. I'm not sure there's much more you can do.
– Evan
Aug 12 '13 at 16:08
add a comment |Â
1 Answer
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The multiplicity of an eigenvalue in the minimal polynomial is the size of that eigenvalue's largest Jordan block. See the "Complex matrices" topic in Wikipedia article "Jordan normal form."
answered Aug 11 at 20:38
Maurice P
1,1601630
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
The multiplicity of an eigenvalue in the minimal polynomial is the size of that eigenvalue's largest Jordan block. See the "Complex matrices" topic in Wikipedia article "Jordan normal form."
answered Aug 11 at 20:38
Maurice P
1,1601630
add a comment |Â
up vote
0
down vote
The multiplicity of an eigenvalue in the minimal polynomial is the size of that eigenvalue's largest Jordan block. See the "Complex matrices" topic in Wikipedia article "Jordan normal form."
answered Aug 11 at 20:38
Maurice P
1,1601630
add a comment |Â
up vote
0
down vote
up vote
0
down vote
The multiplicity of an eigenvalue in the minimal polynomial is the size of that eigenvalue's largest Jordan block. See the "Complex matrices" topic in Wikipedia article "Jordan normal form."
answered Aug 11 at 20:38
Maurice P
1,1601630
The multiplicity of an eigenvalue in the minimal polynomial is the size of that eigenvalue's largest Jordan block. See the "Complex matrices" topic in Wikipedia article "Jordan normal form."
answered Aug 11 at 20:38
Maurice P
1,1601630
answered Aug 11 at 20:38
Maurice P
1,1601630
answered Aug 11 at 20:38
Maurice P
1,1601630
answered Aug 11 at 20:38
Maurice P
1,1601630
1,1601630
add a comment |Â
add a comment |Â
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math.stackexchange.com/questions/82607/… has some information. I'm not sure there's much more you can do.
– Evan
Aug 12 '13 at 16:08