Hi, I have trouble to compute the derivative in $V$ of: $ \frac{VQ}{\|VQ\|_2^2} $ where $V\in\mathbf{R}^{1,q}$ and $Q\in\mathbf{R}^{q,m}$

Dear experts, I am looking for a way to define an "alignment vector" (or anisotropy or orientation vector?) for a given geometrical object. I am not sure how to put this into corr …

The notation for tensors is like the plumbing in a very old Vermont farmhouse. It may once have been intentionally designed, but after that it just evolved. As an example, it seems …

Since points on a euclidean plane can be represented by one coordinate on a space-filling curve, is there any curve such that if two vectors $(x_0,y_0)$ and $(x_1,y_1)$ were repres …

If we consider $\mathbb{R}^{1,3}$ as a vector space with orthogonal geometry $B:\mathbb{R}^{4} \times \mathbb{R}^{4} \rightarrow \mathbb{R} $ it is possible to define a one-to-one …

We have a two sets of vectors ($\mathbb{C}^d$), $A=\{ v_1, \ldots v_n\}$ and $B=\{u_1, \ldots u_n\}$. The question is if there is an efficient solution (polynomial in $n$) for che …

Can you proof that $\mathbf{w} \cdot\mathbf{p}$ is normally distributed, where $\mathbf{w}$ is a random vector where each component is uniformly distributed $[0,1]$ and its $L^1$-n …

So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. If the force is perpendicular to the velocity it will cause the path of the …

Consider sets whose elements are (or can be mapped to) integers in the range [0, N-1]. A popular scheme for representing a set A of this type is by means of a Boolean vector, B, …

Let $S$ be a smooth projective surface with an ample divisor $X\subset S$. Consider the moduli stack of vector bundles $F$ on $S$ such that 1) $c_1(F)=0$ 2) $c_2(F)=n$ 3) The re …

I have say a sample of n p dimensional points and I want to treble the distance between each point and the mean of all the points in continuous parameter space. Does anyone know ho …

Lets say i have a vector X with dimensions a and b and another vector Y of dimensions a and c. Is it possible to calculate cosine similarity between these two vectors? If so, how …

Hi, Could someone explain how does the vector multiplication work in the following example? I don't get it at all. (2,3,-1) x (-3,1,-1) = (-2,5,11) Would appreciate, thanks :)

Let $M$ be a complex $n-$dim manifold and $u : M \rightarrow \mathbb{R}$ be some smooth function. On $M$ assume that we have a Kaehler metric $h$. How is the complex gradient vecto …

It makes perfect sense to me conceptually, but when I try to prove it mathematically I end up going in circles. I've used all the definitions of a dot product and can't seem to fin …