Mixing
find a vector with almost equal projection onto multiple vector
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I have reached to a problem and I appreciate any suggestion to solve this issue. I need to find a vector like $vin mathbb{C}^M$ which has almost same projection onto multiple vectors with the same size, say $h_1,h_2,...,h_N$. Since $N>M$ it does not have a closed form solution. It is very likely that such a vector does not exist. Then, how can I find or search for a vector with this property or a vector with the different projection values within a narrow range?
linear-algebra projective-space projection projection-matrices
asked Jan 21 at 18:05
zstrzstr
11
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add a comment |
$begingroup$
I have reached to a problem and I appreciate any suggestion to solve this issue. I need to find a vector like $vin mathbb{C}^M$ which has almost same projection onto multiple vectors with the same size, say $h_1,h_2,...,h_N$. Since $N>M$ it does not have a closed form solution. It is very likely that such a vector does not exist. Then, how can I find or search for a vector with this property or a vector with the different projection values within a narrow range?
linear-algebra projective-space projection projection-matrices
asked Jan 21 at 18:05
zstrzstr
11
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How about $v=0$? Its projections are all $0$.
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– Robert Israel
Jan 21 at 18:12
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Thanks Robert. The projection should be larger than a small value like $gamma$
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– zstr
Jan 21 at 18:16
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You could do a least squares types of minimization
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– Andrei
Jan 21 at 18:30
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Thanks Andrei. Do you have any idea about the search for such a vector? How can I launch an well-organized search?
$endgroup$
– zstr
Jan 22 at 4:06
add a comment |
$begingroup$
I have reached to a problem and I appreciate any suggestion to solve this issue. I need to find a vector like $vin mathbb{C}^M$ which has almost same projection onto multiple vectors with the same size, say $h_1,h_2,...,h_N$. Since $N>M$ it does not have a closed form solution. It is very likely that such a vector does not exist. Then, how can I find or search for a vector with this property or a vector with the different projection values within a narrow range?
linear-algebra projective-space projection projection-matrices
asked Jan 21 at 18:05
zstrzstr
11
$endgroup$
I have reached to a problem and I appreciate any suggestion to solve this issue. I need to find a vector like $vin mathbb{C}^M$ which has almost same projection onto multiple vectors with the same size, say $h_1,h_2,...,h_N$. Since $N>M$ it does not have a closed form solution. It is very likely that such a vector does not exist. Then, how can I find or search for a vector with this property or a vector with the different projection values within a narrow range?
linear-algebra projective-space projection projection-matrices
linear-algebra projective-space projection projection-matrices
asked Jan 21 at 18:05
zstrzstr
11
asked Jan 21 at 18:05
zstrzstr
11
asked Jan 21 at 18:05
zstrzstr
11
asked Jan 21 at 18:05
zstrzstr
11
asked Jan 21 at 18:05
zstrzstr
11
11
$begingroup$
How about $v=0$? Its projections are all $0$.
$endgroup$
– Robert Israel
Jan 21 at 18:12
$begingroup$
Thanks Robert. The projection should be larger than a small value like $gamma$
$endgroup$
– zstr
Jan 21 at 18:16
$begingroup$
You could do a least squares types of minimization
$endgroup$
– Andrei
Jan 21 at 18:30
$begingroup$
Thanks Andrei. Do you have any idea about the search for such a vector? How can I launch an well-organized search?
$endgroup$
– zstr
Jan 22 at 4:06
add a comment |
$begingroup$
How about $v=0$? Its projections are all $0$.
$endgroup$
– Robert Israel
Jan 21 at 18:12
$begingroup$
Thanks Robert. The projection should be larger than a small value like $gamma$
$endgroup$
– zstr
Jan 21 at 18:16
$begingroup$
You could do a least squares types of minimization
$endgroup$
– Andrei
Jan 21 at 18:30
$begingroup$
Thanks Andrei. Do you have any idea about the search for such a vector? How can I launch an well-organized search?
$endgroup$
– zstr
Jan 22 at 4:06
$begingroup$
How about $v=0$? Its projections are all $0$.
$endgroup$
– Robert Israel
Jan 21 at 18:12
$begingroup$
How about $v=0$? Its projections are all $0$.
$endgroup$
– Robert Israel
Jan 21 at 18:12
$begingroup$
Thanks Robert. The projection should be larger than a small value like $gamma$
$endgroup$
– zstr
Jan 21 at 18:16
$begingroup$
Thanks Robert. The projection should be larger than a small value like $gamma$
$endgroup$
– zstr
Jan 21 at 18:16
$begingroup$
You could do a least squares types of minimization
$endgroup$
– Andrei
Jan 21 at 18:30
$begingroup$
You could do a least squares types of minimization
$endgroup$
– Andrei
Jan 21 at 18:30
$begingroup$
Thanks Andrei. Do you have any idea about the search for such a vector? How can I launch an well-organized search?
$endgroup$
– zstr
Jan 22 at 4:06
$begingroup$
Thanks Andrei. Do you have any idea about the search for such a vector? How can I launch an well-organized search?
$endgroup$
– zstr
Jan 22 at 4:06
add a comment |
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$begingroup$
How about $v=0$? Its projections are all $0$.
$endgroup$
– Robert Israel
Jan 21 at 18:12
$begingroup$
Thanks Robert. The projection should be larger than a small value like $gamma$
$endgroup$
– zstr
Jan 21 at 18:16
$begingroup$
You could do a least squares types of minimization
$endgroup$
– Andrei
Jan 21 at 18:30
$begingroup$
Thanks Andrei. Do you have any idea about the search for such a vector? How can I launch an well-organized search?
$endgroup$
– zstr
Jan 22 at 4:06