i********e
发帖数: 31 | 1 What is the intersection of all isometry groups
of all L_p norms? Is it the identity operator?
Thanks! |
l********e
发帖数: 3632 | 2 你的问题没有看懂。
不过一个流形上绝大多数（open dense）的RIEMAN度量的ISOMETRY GROUP都是只有一个
IDENTITY，不知道是否回答了你的问题。
【在 i********e 的大作中提到】
: What is the intersection of all isometry groups
: of all L_p norms? Is it the identity operator?
: Thanks!
|
l********e
发帖数: 3632 | |
i********e
发帖数: 31 | 4 Thanks.
For example, the isometry group of the L2 norm is
the set of unitary matrices.
the isometry group of the L1 norm is the set
of all matrices that look like permutation
matrices but the +1 entries are replaced
by arbitrary complex numbers on unit circle.
【在 l********e 的大作中提到】
: 你的问题没有看懂。
: 不过一个流形上绝大多数（open dense）的RIEMAN度量的ISOMETRY GROUP都是只有一个
: IDENTITY，不知道是否回答了你的问题。
|
G******i
发帖数: 163 | 5 So you know the permutations, U(1), etc. stuff.
Then how come you still asked
"What is the intersection of all isometry groups
of all L_p norms? Is it the identity operator?"
Didn't you see, for example, the permutations are in
"the intersection of all isometry groups
of all L_p norms"?
【在 i********e 的大作中提到】
: Thanks.
: For example, the isometry group of the L2 norm is
: the set of unitary matrices.
: the isometry group of the L1 norm is the set
: of all matrices that look like permutation
: matrices but the +1 entries are replaced
: by arbitrary complex numbers on unit circle.
|
i********e
发帖数: 31 | 6 My stupid. Thanks!
【在 G******i 的大作中提到】
: So you know the permutations, U(1), etc. stuff.
: Then how come you still asked
: "What is the intersection of all isometry groups
: of all L_p norms? Is it the identity operator?"
: Didn't you see, for example, the permutations are in
: "the intersection of all isometry groups
: of all L_p norms"?
|
