Mathematical vectors, operations on vectors and vectorized programming.

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7
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1answer
469 views

Estimation of vector autoregressive (VAR) process

To estimate 1-dimensional VAR process (which is AR process) you can easily use functions EstimatedProcess or ...
7
votes
2answers
487 views

How to make a point's position time-dependent given a formula for the next step?

I've made a program that is just some points on a plane. Red points are cops and green points are robbers. Each point has a vector indicating where it is going to be in the next step of $t$. Right now ...
0
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0answers
118 views

Gradient from Vectors type

I'm working with Vectors type in Mathematica 9. For this purpose I use the following command: ...
4
votes
2answers
4k views

How to combine two vectors into a matrix by columns?

I know it may sounds idiot, but I've been looking through the document, and couldn't find a way to combine two vectors say {a, b} and ...
1
vote
1answer
229 views

Rotating a set of 3D points against an arbitrary axis

I want to rotate a list of 3D points around unit vector (1,0,1) by the angle of Pi. How can I accomplish it?
2
votes
1answer
296 views

Plot Piecewise-Smooth Vector Field.

I want to plot a piecewise-smooth vector field. For instance: $F_1(x,y) = (x^2 + y^2, y^2)$, $F_2 (x,y) = (2xy,2xy-x^2)$ and $H(x,y) = x-y$ $F(x,y) = \begin{cases} F_1(x,y) \text{ if } H(x,y) ...
0
votes
1answer
171 views

replace is not happening for specific vector valued expression

Given x[t_] := {Subscript[x, 1][t], Subscript[x, 2][t]} following replace works fine x[t] /. x[t] -> 0 0 but following ...
1
vote
2answers
84 views

How do I avoid vector variables being treated as scalars in the course of replacements?

I often work with a mixture of symbolic and concrete values as I develop teaching materials. I introduce variables symbolically and then need to instantiate them to specific values while continuing ...
4
votes
1answer
202 views

Orthogonalizing without normalizing

Is there a way to make Orthogonalize do the normal Gram-Schmidt procedure without normalizing the result? As far as I've understood this was possible with ...
3
votes
1answer
412 views

Plotting a Gravity-Field [duplicate]

I try to plot a 2D gravity field or something similar in the form like $r/|r|^3$ with the standart builtin VectorPlot function: ...
2
votes
2answers
822 views

Circular Orbit Velocity in Vector Components

I'm trying to find out how to calculate the initial velocity needed to keep a spacecraft in a circular orbit around the Earth given its initial position and an initial angle theta in a Cartesian ...
6
votes
2answers
561 views

Plotting: Is anyone familiar with gradientfieldplot command?

I am trying to plot this graph showing the electric field lines and lines of equipotential based off the electrode configuration(in black) of two parallel lines. This is what I've been using for other ...
0
votes
2answers
290 views

Plotting problem

I was wondering why I keep receiving the error message "Derivative should be a triple of numbers, or scaled form" from the following code ...
1
vote
1answer
341 views

Simplify vector expression - is there something like “Factor” for vectors, dot products etc.?

I am looking for a way to simplify dot products etc. Here is a minimal example: Lets say I have two vectors a and b: Array[a,2] Array[b,2] Now I evaluate their ...
1
vote
2answers
724 views

How to input a 3-vector in spherical coordinates?

I would like to input a 3-vectors in spherical coordinates $(r, \theta, \phi)$ and be able to operate on such vectors (dot and cross product) with the results being given in the same spherical ...
1
vote
3answers
780 views

Adding a Sphere onto an existing 3D plot

I have a 3D plot. I need to add a small sphere marking the starting point, r[t] == 0. I'm pretty new at Mathematica and would greatly appreciate some help. ...
4
votes
2answers
172 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my ...
5
votes
0answers
736 views

computation of gradient vector field in 3D using GradientOrientationFilter

I want to compute a 3D gradient vector field of an Image3D object using the built-in GradientOrientationFilter function in Mathematica. From the documentation I ...
4
votes
5answers
336 views

How to generalize and speed up this program?

There is a vector whose length is $n*m$, we can part it into $n$ sections in order. I want to define a function to compare the $i$-th and $i+1$-th section and find the minimum. The program for $n=m=3$ ...
3
votes
2answers
512 views

Ploting a 3D vector field using Manipulate, VectorPlot3D and NDSolve

My aim is to plot a vector field of the following system with a few trajectories: $$r'(t)=i-l.r(t)-\text{ux}. r(t). x(t)-\text{uy}. r(t). y(t) \\ x'(t)=\text{ex}. \text{ux}. r(t). x(t)-\text{mx}. ...
20
votes
7answers
834 views

Make a huge vector in a wise way

I need to construct a vector similar to: v[x_]:={0, 0, x, 0, 0, 2*x, 0, 0, 3*x, ....., 0, 0, n*x}; where n=10^9. How can I ...
1
vote
4answers
334 views

converting between forms - symbols/subscripts - matrix products

If I have a vector of the form (xp+y, x+yp) do you have a simple way of creating the following matrix and vector from it: {{p, 1}, {1, p}} * {x, y}, such that ...
1
vote
1answer
141 views

Linear interpolation between defined anchorpoints in an array (where anchorpoints are set each time we see a new element)

This question is an update and a correction my earlier question: Linear interpolation of a list between periodic anchorpoints (which was nicely answered). Imagine I have a list of the form: ...
0
votes
1answer
250 views

Simplify function with normalized vector

I made a very simple case: testF[x_, y_, z_] = x^2 + y^2 + z^2 Simplify[testF[x, y, z]] If {x, y, z} is normalized, the simplified result should just be 1. How ...
1
vote
2answers
423 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in ...
1
vote
1answer
148 views

Using Select on list of vectors [duplicate]

I have a dataset, where each element in the list is a vector as in data = Table[{i, 2 i, 3 i}, {i, 1, 10}] As an example, I am interested in the entries where ...
2
votes
1answer
621 views

Plot a 3D vector field from a file [duplicate]

I have a data file with six columns {x,y,z} and {ux,uy,uz} respectively, and I would like to plot the 3D vector field. http://www.mediafire.com/download/udoa61hu0m6itrc/campo.txt I'm trying to do ...
3
votes
1answer
737 views

Normal and Tangent of Acceleration in 3D

I need to figure out how to find the Normal and Tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal ...
1
vote
1answer
133 views

Difference between vector's Dimensions

What's the difference between projection= Table[Conjugate[autoVett[[k]].someVector1], {k, 1, r}] Dimensions[projection] that gave me as results ...
6
votes
2answers
624 views

Animated Vector plot

I'm trying to make an animation of a time-varying 2D vector field. However, I'm got a difficulty in that Mathematica normalises the length of the vectors with each call to ...
1
vote
1answer
512 views

Making a ListVectorPlot3D from data in an external file

I have a .dat file with six columns: {x y z vx vy vz}, where x, y, z are space coordinates and vx, vy, vz are the vector components. How can I use this file to get ...
1
vote
1answer
110 views

How to fix the number and length of vectors when using ListVectorPLot

I want to plot only the vectors that I specify in my list of vectors, and no more. ListVectorPlot plots many of them, namely plots the field extrapolating from my four vectors.I would also like to ...
8
votes
2answers
660 views

How to declare a 3D vector variable?

How can I do vector calculations without telling Mathematica the vector entries? I have very many arbitrary linear combinations in $\mathbb{R}^3$ which I want to perform some general calculations on ...
1
vote
2answers
305 views

Doing vector manipulations on Mathematica

This is hopefully a simpler version of this previous unanswered question of mine. Let me just focus on the two expressions $F_2^{(s)}$ and $F_3^{(s)}$ given in A.3 and A.4 of page 19 of this paper. ...
3
votes
1answer
529 views

NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
5
votes
6answers
907 views

A matrix-vector cross product

I want to do a cross product involving a vector of Pauli matrices $\vec \sigma = \left( {{\sigma _1},{\sigma _2},{\sigma _3}} \right)$; for example, $\vec \sigma \times \left( {1,2,3} \right)$. ...
6
votes
1answer
1k views

Smoothing/Averaging 2D Vector Fields

I have a list of 2D vectors defined by {{x,y},{u,v}} and would like to smooth or average the vectors. For example here are 2 vector fields, the second has noise ...
1
vote
1answer
155 views

Splitting list of sums into a sum of lists

I want to split a list of sums into a sum of lists For example, I'd like to turn {{x + y + z}, {x}, {y}, {z}} into ...
0
votes
0answers
160 views

Any way to fully expand an expression of two operators?

I am looking for a way to expand a complicate expression like the follow (A o B + C o (DxE))*(D o (ExF) - ExA + A) Here o and x are the operator. I want to ...
2
votes
2answers
636 views

How to expand a general expression in cross and dot product in Mathematica

I am looking for a way to simply the general expression in cross product and dot product with general vectors. I got a help in How do I simplify a vector expression? but soon I find that it doesn't ...
1
vote
2answers
986 views

How to plot vector function r(t) = i + j + t*k

How can I plot the vector function $r(t) = i + j + t\;k$, where i, j, k are unit vectors, and t is the parameter of the function r.
6
votes
2answers
183 views

Reduce data by taking averages

I am trying to implement the following: I have got two vectors x and y of unequal lengths. The length of ...
5
votes
2answers
1k views

Plot 2D Vector function in 3D

I want to plot a 2D vector function such as $F(x,y) = (a(x,y),\,b(x,y))$ in a 3D graph so that the vectors are embedded in the xy plane. I tried to do the following: First I defined a piecewise ...
2
votes
1answer
137 views

Differentiating with respect to vectors of unspecified length

Given a function defined by f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}] I can easily calculate the derivative for a fixed ...
2
votes
3answers
2k views

Phase space vector field [duplicate]

I have a system of non linear equations and from NDSolve I get the solution. I plot the phase space with ...
0
votes
1answer
198 views

How can I impose a condition on Solve or FullSimplify?

I would like to define a real 3-D vector as, say, v = {x, y, z}, but I want it to have a fixed norm and not necessarily a unit norm. I would like to impose this ...
0
votes
1answer
401 views

How to define a fixed length vector in Mathematica?

I would like to define a 3-D vector as say v={x,y,z}, but I want it to have a fixed norm, say a unit norm |v|=1. How do I impose this condition on v.
1
vote
1answer
170 views

Need assistance with plotting Cell Center Points and Normals (ListPlot, ListVectorPlot)

This is the CellCenter datapoints and associated Normals data: http://wikisend.com/download/458974/CellCenters-and-Normals.dat The dat file contains data points for x,y coordinates and x,y ...
7
votes
2answers
3k views

How do I simplify a vector expression?

I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica: Simplify[Dot[x, y] - Dot[y, x]] I think the ...
1
vote
0answers
93 views

Solving for vector elements in a function to which the vectors are not passed explicitly

I want to define a function which takes in two integers (indicating the lengths of 2 vectors), and solves a simple set of expressions at a set of points to find all the values in both the vectors. so ...