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Oct
28
comment Covariance, covariance operator, and covariance function
Do you mean that $E[ ]: H^*\to R$ is a functional on $H^*$, so it is in $H^{**}$. And $H^{**}=H$. So then $E[]$, as element in $H^{**}$ be represented by m in $H^*$, so then $E[\phi]=<\phi,m>_{H^*}=\phi(m)=<h_{\phi},m>$?
Oct
28
comment Covariance, covariance operator, and covariance function
I mean, why "the mean can be represented by an element in H"? I don't understand this. "A real number(the mean) can be represented by an element in Hilbert space"? (I mean, by Riesz, functional on H can be represented. why here the mean can also be represented?)
Oct
28
comment Covariance, covariance operator, and covariance function
Thank you for your answer! One question about the concept: is the result of the expectation in $R$ or in $X$ or in $X^*$? Is this the same as the mean map or the distribution embedding to RKHS?
Sep
29
awarded  Popular Question
Apr
14
comment find special basis to make null space part equal to zero
Thank you so much for your answer!
Apr
7
accepted Computing bases for direct, wedge, tensor products, etc., of given vector spaces
Apr
7
revised Computing bases for direct, wedge, tensor products, etc., of given vector spaces
added 16 characters in body
Apr
7
comment Computing bases for direct, wedge, tensor products, etc., of given vector spaces
@Travis Thank you for your answer! I fixed (1). For (3), why it is the sum not the product? I think for $(v_i,w_j)$, the first element has $dim(V)$ choices, and the second element has $dim(W)$ choices, so it should be $dim(V)dim(W)$. Am I wrong? BTW, just want to make sure, $V\oplus W$ and $V\times W$ are the same thing, right?
Apr
7
comment Computing bases for direct, wedge, tensor products, etc., of given vector spaces
@DietrichBurde Well, we can assume that, since my actual problem is just about finite dimension.
Apr
7
revised Computing bases for direct, wedge, tensor products, etc., of given vector spaces
added 9 characters in body
Apr
7
asked Computing bases for direct, wedge, tensor products, etc., of given vector spaces
Apr
7
comment example for torsion free but not cyclic group
OK, thank you so much for your help!
Apr
7
comment example for torsion free but not cyclic group
Thank you for your answer! One more question, the converse is not true(torsion free is not all free abelian group), right? As you mentioned in the last sentence, counterexample can be considered among those not finitely generated torsion-free abelian groups. Is $\mathbb{Z}^{\infty}$ a such example(torsion-free but not free abelian group)?
Apr
7
accepted example for torsion free but not cyclic group
Apr
6
comment example for torsion free but not cyclic group
Thank you very much!
Apr
6
asked example for torsion free but not cyclic group
Apr
6
comment Find Jordan canonical form with Kronecker product of JCF
I found a good notes digitalcommons.unf.edu/cgi/… But I don't know how to use it(page 48 Thm 56). My problem is such a corner case, with all the eigenvalue 2 and not diagonalizable.
Apr
6
asked Find Jordan canonical form with Kronecker product of JCF
Apr
6
asked use universal properties to prove the existence of isomorphism
Apr
6
accepted find special basis to make null space part equal to zero