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 1d answered Normed Linear Space ,$p \neq 2$ is $\left \| f\right \|_{p}= \sqrt{f,f}$ for each $f \in L^P([0,1])$? 2d comment Theoretical link between the graph diffusion/heat kernel and spectral clustering There is absolutely a link. Have a look at Mauro Maggioni's website and publications to get started, if no one else answers I might give a better answer later. Nov 20 comment Matrix functions of a non-diagonalizable matrix Right, thanks. Edited. Nov 20 revised Matrix functions of a non-diagonalizable matrix deleted 2 characters in body Nov 20 revised Matrix functions of a non-diagonalizable matrix added 17 characters in body Nov 20 answered Matrix functions of a non-diagonalizable matrix Nov 18 answered Simple definition of a positive definite matrix Nov 18 comment Closed convex set as the intersection of (tangent) half spaces Supporting hyperplanes aren't unique for arbitrary convex sets, I'm not sure where you've seen that. They're unique for strictly convex sets. The theorem about half-space intersection doesn't require uniqueness anyway. Nov 18 answered Closed convex set as the intersection of (tangent) half spaces Nov 18 comment reference request for a book on high dimensional probability and data analysis written for mathematicians I doubt that a comprehensive book exists yet, high dimensional data analysis is relatively new. Tao can write a clear, cohesive volume on analysis because real analysis has been very well developed over the last 100+ years. I would recommend getting familiar with rigorous probability (Billingsley) and stats theory (Wasserman) then reading current research articles. Nov 18 comment Operator between Hilbert spaces, boundness, image and eigenvalues Looks like you might be missing an exponent of $2$ in your definition of $H$. Nov 18 comment What does it mean “Distance between $k$-planes induced by the identification plane-projection matrix”? I posted a picture and a link to a MO post, hopefully it helps. Nov 18 revised What does it mean “Distance between $k$-planes induced by the identification plane-projection matrix”? added 384 characters in body Nov 18 comment What does it mean “Distance between $k$-planes induced by the identification plane-projection matrix”? See edit - I wasn't quite careful enough at first. You use the projection onto the subspaces, not onto the planes themselves. The projection onto the shifted plane isn't a linear operator so you can't do an operator norm on it. Nov 18 revised What does it mean “Distance between $k$-planes induced by the identification plane-projection matrix”? deleted 181 characters in body Nov 18 comment What does it mean “Distance between $k$-planes induced by the identification plane-projection matrix”? That would be one way to define it, correct. I tend to prefer to sup over the unit sphere (i.e. $\vert x\vert = 1$), but either works. Presumably they're working with the Euclidean inner product, i.e. $\vert x-y\vert$ means the usual thing, but if they had some strange inner product you'd have to be slightly more careful. Nov 18 answered What does it mean “Distance between $k$-planes induced by the identification plane-projection matrix”? Nov 18 comment Measure of the irrational numbers? Welcome to the wild and wacky jungle of mathematical analysis! Stick with it, it all becomes clear in time. Nov 16 revised Eigenvectors of $AA^T$ as linear linear combinations of columns of $A$ added 39 characters in body Nov 16 answered Eigenvectors of $AA^T$ as linear linear combinations of columns of $A$