Relation between invariant Subspace and characteristic polynomial
$begingroup$
Let V be a complext vector space of dimension=4:
$f in End(V)$ with characteristic polynomial $p_{f}(t)= (t − 1)^2.
(t − 2)^2
$
Define $X$ as the set of W subspace of V such that dim W=2 and W is f-invariant.
If $|X|$ is finite then $|X|$=3.
I tried to work it out using the 4 possible canonical Jordan form of $f$ and relating them to the minimal polynomial, yet I'm not sure about my work.
linear-algebra
asked Jan 12 at 11:53
SMCSMC
6010
$endgroup$
add a comment |
$begingroup$
Let V be a complext vector space of dimension=4:
$f in End(V)$ with characteristic polynomial $p_{f}(t)= (t − 1)^2.
(t − 2)^2
$
Define $X$ as the set of W subspace of V such that dim W=2 and W is f-invariant.
If $|X|$ is finite then $|X|$=3.
I tried to work it out using the 4 possible canonical Jordan form of $f$ and relating them to the minimal polynomial, yet I'm not sure about my work.
linear-algebra
asked Jan 12 at 11:53
SMCSMC
6010
$endgroup$
add a comment |
$begingroup$
Let V be a complext vector space of dimension=4:
$f in End(V)$ with characteristic polynomial $p_{f}(t)= (t − 1)^2.
(t − 2)^2
$
Define $X$ as the set of W subspace of V such that dim W=2 and W is f-invariant.
If $|X|$ is finite then $|X|$=3.
I tried to work it out using the 4 possible canonical Jordan form of $f$ and relating them to the minimal polynomial, yet I'm not sure about my work.
linear-algebra
asked Jan 12 at 11:53
SMCSMC
6010
$endgroup$
Let V be a complext vector space of dimension=4:
$f in End(V)$ with characteristic polynomial $p_{f}(t)= (t − 1)^2.
(t − 2)^2
$
Define $X$ as the set of W subspace of V such that dim W=2 and W is f-invariant.
If $|X|$ is finite then $|X|$=3.
I tried to work it out using the 4 possible canonical Jordan form of $f$ and relating them to the minimal polynomial, yet I'm not sure about my work.
linear-algebra
linear-algebra
asked Jan 12 at 11:53
SMCSMC
6010
asked Jan 12 at 11:53
SMCSMC
6010
asked Jan 12 at 11:53
SMCSMC
6010
asked Jan 12 at 11:53
SMCSMC
6010
asked Jan 12 at 11:53
SMCSMC
6010
6010
add a comment |
add a comment |
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