Name for “the kernel lemma”?
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Lately I've been fascinated by the result that one might state slightly informally
Lemma. (In the context of linear algebra over a field.) If $p$ and $q$ are relatively prime polynomials and $T$ is a linear operator then $ker(pq(T))=ker(p(T))oplusker(q(T))$.
Follows easily from the fact that $F[x]$ is a PID; you can use it to start a proof of the existence of the Jordan Canonical Form, also for a proof that the solution to a constant-coefficient linear homogeneous DE is what it is.
Q: Does this result have a standard name? Or do we know who proved it?
linear-algebra abstract-algebra reference-request math-history
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
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add a comment |
$begingroup$
Lately I've been fascinated by the result that one might state slightly informally
Lemma. (In the context of linear algebra over a field.) If $p$ and $q$ are relatively prime polynomials and $T$ is a linear operator then $ker(pq(T))=ker(p(T))oplusker(q(T))$.
Follows easily from the fact that $F[x]$ is a PID; you can use it to start a proof of the existence of the Jordan Canonical Form, also for a proof that the solution to a constant-coefficient linear homogeneous DE is what it is.
Q: Does this result have a standard name? Or do we know who proved it?
linear-algebra abstract-algebra reference-request math-history
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
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2
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In my university it was called "primary decomposition", in fact it is a corollary of en.wikipedia.org/wiki/Primary_decomposition.
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– Ivan Di Liberti
Jan 17 at 16:04
add a comment |
$begingroup$
Lately I've been fascinated by the result that one might state slightly informally
Lemma. (In the context of linear algebra over a field.) If $p$ and $q$ are relatively prime polynomials and $T$ is a linear operator then $ker(pq(T))=ker(p(T))oplusker(q(T))$.
Follows easily from the fact that $F[x]$ is a PID; you can use it to start a proof of the existence of the Jordan Canonical Form, also for a proof that the solution to a constant-coefficient linear homogeneous DE is what it is.
Q: Does this result have a standard name? Or do we know who proved it?
linear-algebra abstract-algebra reference-request math-history
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
$endgroup$
Lately I've been fascinated by the result that one might state slightly informally
Lemma. (In the context of linear algebra over a field.) If $p$ and $q$ are relatively prime polynomials and $T$ is a linear operator then $ker(pq(T))=ker(p(T))oplusker(q(T))$.
Follows easily from the fact that $F[x]$ is a PID; you can use it to start a proof of the existence of the Jordan Canonical Form, also for a proof that the solution to a constant-coefficient linear homogeneous DE is what it is.
Q: Does this result have a standard name? Or do we know who proved it?
linear-algebra abstract-algebra reference-request math-history
linear-algebra abstract-algebra reference-request math-history
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
edited Jan 17 at 17:20
user635162
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
asked Jan 17 at 16:00
David C. UllrichDavid C. Ullrich
61.8k44095
61.8k44095
2
$begingroup$
In my university it was called "primary decomposition", in fact it is a corollary of en.wikipedia.org/wiki/Primary_decomposition.
$endgroup$
– Ivan Di Liberti
Jan 17 at 16:04
add a comment |
2
$begingroup$
In my university it was called "primary decomposition", in fact it is a corollary of en.wikipedia.org/wiki/Primary_decomposition.
$endgroup$
– Ivan Di Liberti
Jan 17 at 16:04
2
2
$begingroup$
In my university it was called "primary decomposition", in fact it is a corollary of en.wikipedia.org/wiki/Primary_decomposition.
$endgroup$
– Ivan Di Liberti
Jan 17 at 16:04
$begingroup$
In my university it was called "primary decomposition", in fact it is a corollary of en.wikipedia.org/wiki/Primary_decomposition.
$endgroup$
– Ivan Di Liberti
Jan 17 at 16:04
add a comment |
1 Answer
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In French schools and universities it is called "Lemme des Noyaux" which is a translation of Kernel Lemma. It is one of the rare occasions where I find a page inthe french wikipedia with no english counterpart.
Here is a link to said page :
https://fr.wikipedia.org/wiki/Lemme_des_noyaux
I suspect it has its own page because it is a standard result in the linear algebra curriculum. Sadly i haven't found a name in english but calling it the Kernel Lemma is a good idea.
answered Jan 18 at 16:59
NassoumoNassoumo
812
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$begingroup$
In French schools and universities it is called "Lemme des Noyaux" which is a translation of Kernel Lemma. It is one of the rare occasions where I find a page inthe french wikipedia with no english counterpart.
Here is a link to said page :
https://fr.wikipedia.org/wiki/Lemme_des_noyaux
I suspect it has its own page because it is a standard result in the linear algebra curriculum. Sadly i haven't found a name in english but calling it the Kernel Lemma is a good idea.
answered Jan 18 at 16:59
NassoumoNassoumo
812
$endgroup$
add a comment |
$begingroup$
In French schools and universities it is called "Lemme des Noyaux" which is a translation of Kernel Lemma. It is one of the rare occasions where I find a page inthe french wikipedia with no english counterpart.
Here is a link to said page :
https://fr.wikipedia.org/wiki/Lemme_des_noyaux
I suspect it has its own page because it is a standard result in the linear algebra curriculum. Sadly i haven't found a name in english but calling it the Kernel Lemma is a good idea.
answered Jan 18 at 16:59
NassoumoNassoumo
812
$endgroup$
add a comment |
$begingroup$
In French schools and universities it is called "Lemme des Noyaux" which is a translation of Kernel Lemma. It is one of the rare occasions where I find a page inthe french wikipedia with no english counterpart.
Here is a link to said page :
https://fr.wikipedia.org/wiki/Lemme_des_noyaux
I suspect it has its own page because it is a standard result in the linear algebra curriculum. Sadly i haven't found a name in english but calling it the Kernel Lemma is a good idea.
answered Jan 18 at 16:59
NassoumoNassoumo
812
$endgroup$
In French schools and universities it is called "Lemme des Noyaux" which is a translation of Kernel Lemma. It is one of the rare occasions where I find a page inthe french wikipedia with no english counterpart.
Here is a link to said page :
https://fr.wikipedia.org/wiki/Lemme_des_noyaux
I suspect it has its own page because it is a standard result in the linear algebra curriculum. Sadly i haven't found a name in english but calling it the Kernel Lemma is a good idea.
answered Jan 18 at 16:59
NassoumoNassoumo
812
answered Jan 18 at 16:59
NassoumoNassoumo
812
answered Jan 18 at 16:59
NassoumoNassoumo
812
answered Jan 18 at 16:59
NassoumoNassoumo
812
812
add a comment |
add a comment |
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In my university it was called "primary decomposition", in fact it is a corollary of en.wikipedia.org/wiki/Primary_decomposition.
$endgroup$
– Ivan Di Liberti
Jan 17 at 16:04