Showing a map between complex vector spaces is surjective
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I am trying to solve the next problem, but I have little clue on how to attack it. Can anybody help me out with a solution or a suggestion on how to attack this type of problems?
Let $V$ and $W$ be finite dimensional complex vector spaces of dimension $m$ and $n$ respectivel and let $A$ and $B$ be linear maps $V rightarrow W$ with $A$ surjective. Show that $A + tB$ is surjective for all but at most $n$ values of $tin mathbb{C}$.
Thanks in advance!
linear-algebra vector-spaces
asked Jan 1 at 23:46
user284639user284639
16919
$endgroup$
|
show 4 more comments
$begingroup$
I am trying to solve the next problem, but I have little clue on how to attack it. Can anybody help me out with a solution or a suggestion on how to attack this type of problems?
Let $V$ and $W$ be finite dimensional complex vector spaces of dimension $m$ and $n$ respectivel and let $A$ and $B$ be linear maps $V rightarrow W$ with $A$ surjective. Show that $A + tB$ is surjective for all but at most $n$ values of $tin mathbb{C}$.
Thanks in advance!
linear-algebra vector-spaces
asked Jan 1 at 23:46
user284639user284639
16919
$endgroup$
$begingroup$
Where is $f$ used?
$endgroup$
– John Douma
Jan 2 at 0:00
$begingroup$
I'm not sure @JohnDouma, I copied the question as I found it.
$endgroup$
– user284639
Jan 2 at 0:04
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I'm voting to close this question as off-topic because the inquirer doesn't seem to understand the details of his/her question.
$endgroup$
– John Douma
Jan 2 at 0:11
1
$begingroup$
@hardmath In general, I agree. In this case, I asked what $f$ was for and the OP said that he didn't know. He said he copied it as he found it. I will certainly retract my close vote if anything changes.
$endgroup$
– John Douma
Jan 2 at 1:24
1
$begingroup$
I have retracted my close vote because you have clarified the problem. However, as I am sure you know, you should include your thoughts on the problem including any work you have done.
$endgroup$
– John Douma
Jan 2 at 1:45
|
show 4 more comments
$begingroup$
I am trying to solve the next problem, but I have little clue on how to attack it. Can anybody help me out with a solution or a suggestion on how to attack this type of problems?
Let $V$ and $W$ be finite dimensional complex vector spaces of dimension $m$ and $n$ respectivel and let $A$ and $B$ be linear maps $V rightarrow W$ with $A$ surjective. Show that $A + tB$ is surjective for all but at most $n$ values of $tin mathbb{C}$.
Thanks in advance!
linear-algebra vector-spaces
asked Jan 1 at 23:46
user284639user284639
16919
$endgroup$
I am trying to solve the next problem, but I have little clue on how to attack it. Can anybody help me out with a solution or a suggestion on how to attack this type of problems?
Let $V$ and $W$ be finite dimensional complex vector spaces of dimension $m$ and $n$ respectivel and let $A$ and $B$ be linear maps $V rightarrow W$ with $A$ surjective. Show that $A + tB$ is surjective for all but at most $n$ values of $tin mathbb{C}$.
Thanks in advance!
linear-algebra vector-spaces
linear-algebra vector-spaces
asked Jan 1 at 23:46
user284639user284639
16919
asked Jan 1 at 23:46
user284639user284639
16919
edited Jan 2 at 1:41
user284639
asked Jan 1 at 23:46
user284639user284639
16919
asked Jan 1 at 23:46
user284639user284639
16919
asked Jan 1 at 23:46
user284639user284639
16919
16919
$begingroup$
Where is $f$ used?
$endgroup$
– John Douma
Jan 2 at 0:00
$begingroup$
I'm not sure @JohnDouma, I copied the question as I found it.
$endgroup$
– user284639
Jan 2 at 0:04
$begingroup$
I'm voting to close this question as off-topic because the inquirer doesn't seem to understand the details of his/her question.
$endgroup$
– John Douma
Jan 2 at 0:11
1
$begingroup$
@hardmath In general, I agree. In this case, I asked what $f$ was for and the OP said that he didn't know. He said he copied it as he found it. I will certainly retract my close vote if anything changes.
$endgroup$
– John Douma
Jan 2 at 1:24
1
$begingroup$
I have retracted my close vote because you have clarified the problem. However, as I am sure you know, you should include your thoughts on the problem including any work you have done.
$endgroup$
– John Douma
Jan 2 at 1:45
|
show 4 more comments
$begingroup$
Where is $f$ used?
$endgroup$
– John Douma
Jan 2 at 0:00
$begingroup$
I'm not sure @JohnDouma, I copied the question as I found it.
$endgroup$
– user284639
Jan 2 at 0:04
$begingroup$
I'm voting to close this question as off-topic because the inquirer doesn't seem to understand the details of his/her question.
$endgroup$
– John Douma
Jan 2 at 0:11
1
$begingroup$
@hardmath In general, I agree. In this case, I asked what $f$ was for and the OP said that he didn't know. He said he copied it as he found it. I will certainly retract my close vote if anything changes.
$endgroup$
– John Douma
Jan 2 at 1:24
1
$begingroup$
I have retracted my close vote because you have clarified the problem. However, as I am sure you know, you should include your thoughts on the problem including any work you have done.
$endgroup$
– John Douma
Jan 2 at 1:45
$begingroup$
Where is $f$ used?
$endgroup$
– John Douma
Jan 2 at 0:00
$begingroup$
Where is $f$ used?
$endgroup$
– John Douma
Jan 2 at 0:00
$begingroup$
I'm not sure @JohnDouma, I copied the question as I found it.
$endgroup$
– user284639
Jan 2 at 0:04
$begingroup$
I'm not sure @JohnDouma, I copied the question as I found it.
$endgroup$
– user284639
Jan 2 at 0:04
$begingroup$
I'm voting to close this question as off-topic because the inquirer doesn't seem to understand the details of his/her question.
$endgroup$
– John Douma
Jan 2 at 0:11
$begingroup$
I'm voting to close this question as off-topic because the inquirer doesn't seem to understand the details of his/her question.
$endgroup$
– John Douma
Jan 2 at 0:11
1
1
$begingroup$
@hardmath In general, I agree. In this case, I asked what $f$ was for and the OP said that he didn't know. He said he copied it as he found it. I will certainly retract my close vote if anything changes.
$endgroup$
– John Douma
Jan 2 at 1:24
$begingroup$
@hardmath In general, I agree. In this case, I asked what $f$ was for and the OP said that he didn't know. He said he copied it as he found it. I will certainly retract my close vote if anything changes.
$endgroup$
– John Douma
Jan 2 at 1:24
1
1
$begingroup$
I have retracted my close vote because you have clarified the problem. However, as I am sure you know, you should include your thoughts on the problem including any work you have done.
$endgroup$
– John Douma
Jan 2 at 1:45
$begingroup$
I have retracted my close vote because you have clarified the problem. However, as I am sure you know, you should include your thoughts on the problem including any work you have done.
$endgroup$
– John Douma
Jan 2 at 1:45
|
show 4 more comments
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$begingroup$
Where is $f$ used?
$endgroup$
– John Douma
Jan 2 at 0:00
$begingroup$
I'm not sure @JohnDouma, I copied the question as I found it.
$endgroup$
– user284639
Jan 2 at 0:04
$begingroup$
I'm voting to close this question as off-topic because the inquirer doesn't seem to understand the details of his/her question.
$endgroup$
– John Douma
Jan 2 at 0:11
1
$begingroup$
@hardmath In general, I agree. In this case, I asked what $f$ was for and the OP said that he didn't know. He said he copied it as he found it. I will certainly retract my close vote if anything changes.
$endgroup$
– John Douma
Jan 2 at 1:24
1
$begingroup$
I have retracted my close vote because you have clarified the problem. However, as I am sure you know, you should include your thoughts on the problem including any work you have done.
$endgroup$
– John Douma
Jan 2 at 1:45