What are situations where one can conclude that all entries of an intersection form are divisible by an integer? More precisely: $F \subset S$ is a proper connected (usually red …

Consider the following exponential kernel: $k(x_1, x_2) = \exp\left(\frac{|x_1 - x_2|}{L}\right)$, which is symmetric and non-negative definite. By virtue of Mercer's theorem, we …

I know that Crammer's decomposition theorem says that any normal distribution can be expressed as the sum of multiple normal distributions. I have been searching for a method to di …

Let $X$ be a set. Let $\mathcal{R}$ be a set of subsets of $X$ such that $\{\} \in \mathcal{R}$ and For all members $A$ and $B$ of $\mathcal{R}$, $\;\; (A\cup B)-(A\cap B) \; \in …

what is the computational complexity of eigenvalue decomposition for a unitary matrix? is O(n^3) a correct answer?

(aka, what I'd meant to ask here) Let $X$ be a set. $\:$ Let $\mathcal{R}$ be a non-empty subset of $2^X$. $\:$ Suppose $\mathcal{R}$ is a delta-ring. Let $\: \phi : \mathcal{R} …

Hello mathoverflow community ! I have a simple question that seems to have a non trivial answer. Given a discrete one dimensional signal $w(x)$ defined in a finite range, and the …

Is it possible to analytically derive SVD or PD of a given matrix in terms of the matrix elements given as variables? Edit: My apologies for not making the question clear. As some …

In an earlier post (Use Lie Sub-Groups of GL(3, R) for elastic deformation ? here), I mentioned polar decompositions as in F = RU where R in SO(3) & U in symmetric positive-sem …

The decomposition theorem states roughly, that the pushforward of an IC complex, along a proper map decomposes into a direct sum of shifted IC complexes. Are there special cases f …

There's an important piece of geometric knowledge usually quoted as Beilinson-Bernstein-Deligne. Here's a refresher: by $IC$ one means the intersection complex, which is just $\ma …

Which statement is usually called the Decomposition Theorem (for perverse sheaves)? Is this (roughly): a proper pushforward of an intersection complex could be decomposed into a di …

I saw the statement of the decomposition theorem for perverse sheaves sometime ago. I know that (modulo most of the details) it implies some big theorems in algebraic geometry and …

I have a set of positive integers $a$, where $\displaystyle\sum_i{a_i}=700$ and $\displaystyle\sum_i{a_i^2}=1212$. Is there a unique decomposition of $a$ and, if so, how do I reco …

This is a follow-up to this post on the Decomposition Theorem. Hopefully, this will also invite some discussion about the theorem and perverse sheaves in general. My question is h …