# Questions tagged [vector]

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### In Lanczos algorithm, can we choose the staring vector to be the first eigenvector of the input matrix A?

In Lanczos algorithm, can we choose the staring vector $v$ to be the first eigenvector of the input matrix $A$? How can we select it? and why $v$ need to have norm 1?
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### Vector Form Using the Curl (Line Integral ) in Python

There is an example in Vector Calculus from Madsen & Tromba page 435 that states: Let $F=(xy^2,y+x)$.Integrate $(\nabla \times F)\cdot k$ over the region in the first quadrant bounded by the ...
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### Vector characterization of cylinder displacements in a box

We have a cylinder of length $l$ (in units of its radius $d,$ as basic unit of length set to $d=1.$) in a box, and we consider an orthonormal Cartesian coordinate system with its origin placed at the ...
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### Software/code to extract a solenoidal (a.k.a. divergence-free) field from a 2D vector field numerically

Can somebody point me to software/code to extract a solenoidal (a.k.a. divergence-free) field from a 2D vector field numerically? There are a plethora of papers and documents describing how to do ...
683 views

### Find a permutation matrix (using the Matlab's function $symrcm$) of a matrix $A(2:end, 2:end)$

I've the following Matlab code: r = symrcm(A(2:end, 2:end)); prcm = [1 r + 1]; spy(A(prcm, prcm)); where A should be sparse ...
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### two level iterators C++ [closed]

I am trying to implement a two level iterator as I will now describe. Basically I have a "vector of vectors" and I want a single iterator that will loop over all the objects in the vector of vectors. ...
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### Regarding solution vector of the wave equation

I am simulating the wave equation using FEM. For a 2D wave equation, when I visualise my output in Paraview, I see a separate solution in 'x' and 'y' direction for each node on the mesh. Therefore, if ...
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### Efficiently approximating sum of 2-norms

Suppose I have a real vector $\bf x$ of length $KN$, where $K<<N$. Let's say I break this vector $\bf x$ up into $N$ vectors each of length $K$, $${\bf x}_1,...{\bf x}_n.$$ Now I would like ...
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### Numerically calculating the divergence of a set of oriented points

Say I have a set of oriented points at locations $\vec{v_i}$ with each some direction $\vec{n_i}$, in practice they represent the normals of some surface that has been non uniformly sampled. How would ...
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### How can I efficiently position the different segments of a large vector in Eigen C++?

I have a very large(up to 9 000 000) VectorXi vector defined in Eigen C++ which is read from a data file. The vector consists of 0, 1, 2, ...n segments with ...
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### combine $n$ vectors using $L2-normalization$

Suppose that I have the following vectors $v_1$, $v_2$, $v_3$ $\in R^n$,$n= 9$. What I want to do exactly is to combine these $3$ vectors into $1$ representative vector $V$. According to the ...