## Tagged Questions

38 views

### vector derivative of $\frac{VQ}{\|VQ\|_2^2}$ [closed]

Hi, I have trouble to compute the derivative in $V$ of: $\frac{VQ}{\|VQ\|_2^2}$ where $V\in\mathbf{R}^{1,q}$ and $Q\in\mathbf{R}^{q,m}$
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### How to define an “anisotropic vector” for a given object?

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 …
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### How many flavors should a notational system offer for rank-1 tensors?

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 …
209 views

### Space filling curve to simplify vector addition? [closed]

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 …
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### Matrix associated to a vector

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 …
252 views

### Sets of vectors related by a rotation

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 …
265 views

### Proof normal distribution of dot product, with a uniform distributed vector [closed]

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 …
1k views

### How Does force relate to velocity [closed]

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 …
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### Algorithm for union, intersection and subtraction help? [closed]

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, …
492 views

### moduli of vector bundles on a surface

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 …
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### Trebling the distance between 2 points in a continuous parameter space ? [closed]

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 …
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### Can cosine similarity calculation for vectors of different dimensions [closed]

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 …
112 views

### Multiplying vectors [closed]

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 …