Rotation Matrix from l1 to l_infinity
1
$begingroup$
Both the ell_1 unit ball and ell_infinity unit ball are cubes.
What scaling factor and rotation matrix that will map one of these cubes to the other?
linear-algebra
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
$endgroup$
add a comment |
1
$begingroup$
Both the ell_1 unit ball and ell_infinity unit ball are cubes.
What scaling factor and rotation matrix that will map one of these cubes to the other?
linear-algebra
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
$endgroup$
1
$begingroup$
Notice that this is only possible in two dimensions. Already in three dimensions the L1 ball has six corners while the l_infty ball has 8.
$endgroup$
– Thomas Ahle
Dec 28 '18 at 22:24
$begingroup$
Thanks. Does it make sense to ask if there is a (non-bijection) function from L1 to L_infty?
$endgroup$
– Dan Feldman
Dec 28 '18 at 23:05
$begingroup$
You can embed $ell_1$ into $ell_infty$. A cute way to do this is using exponentially distributed random variables. See also kam.mff.cuni.cz/~matousek/ba-a4.pdf for more stuff like this.
$endgroup$
– Thomas Ahle
Dec 29 '18 at 20:40
add a comment |
1
1
1
$begingroup$
Both the ell_1 unit ball and ell_infinity unit ball are cubes.
What scaling factor and rotation matrix that will map one of these cubes to the other?
linear-algebra
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
$endgroup$
Both the ell_1 unit ball and ell_infinity unit ball are cubes.
What scaling factor and rotation matrix that will map one of these cubes to the other?
linear-algebra
linear-algebra
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
asked Dec 28 '18 at 22:12
Dan FeldmanDan Feldman
262
262
1
$begingroup$
Notice that this is only possible in two dimensions. Already in three dimensions the L1 ball has six corners while the l_infty ball has 8.
$endgroup$
– Thomas Ahle
Dec 28 '18 at 22:24
$begingroup$
Thanks. Does it make sense to ask if there is a (non-bijection) function from L1 to L_infty?
$endgroup$
– Dan Feldman
Dec 28 '18 at 23:05
$begingroup$
You can embed $ell_1$ into $ell_infty$. A cute way to do this is using exponentially distributed random variables. See also kam.mff.cuni.cz/~matousek/ba-a4.pdf for more stuff like this.
$endgroup$
– Thomas Ahle
Dec 29 '18 at 20:40
add a comment |
1
$begingroup$
Notice that this is only possible in two dimensions. Already in three dimensions the L1 ball has six corners while the l_infty ball has 8.
$endgroup$
– Thomas Ahle
Dec 28 '18 at 22:24
$begingroup$
Thanks. Does it make sense to ask if there is a (non-bijection) function from L1 to L_infty?
$endgroup$
– Dan Feldman
Dec 28 '18 at 23:05
$begingroup$
You can embed $ell_1$ into $ell_infty$. A cute way to do this is using exponentially distributed random variables. See also kam.mff.cuni.cz/~matousek/ba-a4.pdf for more stuff like this.
$endgroup$
– Thomas Ahle
Dec 29 '18 at 20:40
1
1
$begingroup$
Notice that this is only possible in two dimensions. Already in three dimensions the L1 ball has six corners while the l_infty ball has 8.
$endgroup$
– Thomas Ahle
Dec 28 '18 at 22:24
$begingroup$
Notice that this is only possible in two dimensions. Already in three dimensions the L1 ball has six corners while the l_infty ball has 8.
$endgroup$
– Thomas Ahle
Dec 28 '18 at 22:24
$begingroup$
Thanks. Does it make sense to ask if there is a (non-bijection) function from L1 to L_infty?
$endgroup$
– Dan Feldman
Dec 28 '18 at 23:05
$begingroup$
Thanks. Does it make sense to ask if there is a (non-bijection) function from L1 to L_infty?
$endgroup$
– Dan Feldman
Dec 28 '18 at 23:05
$begingroup$
You can embed $ell_1$ into $ell_infty$. A cute way to do this is using exponentially distributed random variables. See also kam.mff.cuni.cz/~matousek/ba-a4.pdf for more stuff like this.
$endgroup$
– Thomas Ahle
Dec 29 '18 at 20:40
$begingroup$
You can embed $ell_1$ into $ell_infty$. A cute way to do this is using exponentially distributed random variables. See also kam.mff.cuni.cz/~matousek/ba-a4.pdf for more stuff like this.
$endgroup$
– Thomas Ahle
Dec 29 '18 at 20:40
add a comment |
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1
$begingroup$
Notice that this is only possible in two dimensions. Already in three dimensions the L1 ball has six corners while the l_infty ball has 8.
$endgroup$
– Thomas Ahle
Dec 28 '18 at 22:24
$begingroup$
Thanks. Does it make sense to ask if there is a (non-bijection) function from L1 to L_infty?
$endgroup$
– Dan Feldman
Dec 28 '18 at 23:05
$begingroup$
You can embed $ell_1$ into $ell_infty$. A cute way to do this is using exponentially distributed random variables. See also kam.mff.cuni.cz/~matousek/ba-a4.pdf for more stuff like this.
$endgroup$
– Thomas Ahle
Dec 29 '18 at 20:40