Projection onto intersection of affine subspaces
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I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
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add a comment |
$begingroup$
I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
$endgroup$
$begingroup$
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
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– aleph_two
Dec 17 '18 at 4:23
$begingroup$
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
$endgroup$
– InspectorPing
Dec 17 '18 at 14:33
add a comment |
$begingroup$
I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
$endgroup$
I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
linear-algebra
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
asked Nov 15 '18 at 19:59
InspectorPingInspectorPing
1148
1148
$begingroup$
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
$endgroup$
– aleph_two
Dec 17 '18 at 4:23
$begingroup$
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
$endgroup$
– InspectorPing
Dec 17 '18 at 14:33
add a comment |
$begingroup$
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
$endgroup$
– aleph_two
Dec 17 '18 at 4:23
$begingroup$
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
$endgroup$
– InspectorPing
Dec 17 '18 at 14:33
$begingroup$
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
$endgroup$
– aleph_two
Dec 17 '18 at 4:23
$begingroup$
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
$endgroup$
– aleph_two
Dec 17 '18 at 4:23
$begingroup$
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
$endgroup$
– InspectorPing
Dec 17 '18 at 14:33
$begingroup$
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
$endgroup$
– InspectorPing
Dec 17 '18 at 14:33
add a comment |
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$begingroup$
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
$endgroup$
– aleph_two
Dec 17 '18 at 4:23
$begingroup$
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
$endgroup$
– InspectorPing
Dec 17 '18 at 14:33