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Apr
29
asked integration with singular continuous measure in high(two) dimensions
Apr
26
asked integration with delta function
Mar
27
comment positive definite of a matrix(diagonal decay)
Hi @JackD'Aurizio, thanks for your insightful comment! Could you please elaborate a little bit about why you want to use this theorem? Is it a tool to bound the eigenvalues of the above matrix? What it the projection matrix $P$ in this case?
Mar
27
asked characteristic polynomial of linear combination of two matrices
Mar
27
comment positive definite of a matrix(diagonal decay)
BTW, how did you find the determinant(so quickly)? from the above row/column operation to upper/lower triangular matrix? Thanks!
Mar
27
accepted positive definite of a matrix(diagonal decay)
Mar
27
comment positive definite of a matrix(diagonal decay)
Thanks! This decomposition is interesting and I think it may help for further analysis the properties of this matrix.
Mar
27
comment positive definite of a matrix(diagonal decay)
OK, so then only preserve determinant(product of eigenvalues). Does it preserve the sign of eigenvalues? Seems I need to check my linear algebra textbook once more...
Mar
27
comment positive definite of a matrix(diagonal decay)
Seems true. It preserves determinant and similarity(but not char. poly.), right?
Mar
27
comment positive definite of a matrix(diagonal decay)
Thanks. This solves the problem(and can help find the determinant).
Mar
27
comment positive definite of a matrix(diagonal decay)
Thanks! This solves the problem!
Mar
27
asked positive definite of a matrix(diagonal decay)
Mar
14
awarded  Notable Question
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
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