Mathematical vectors, operations on vectors and vectorized programming.
0
votes
2answers
127 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. ...
2
votes
1answer
52 views
NDSolve with vector function
(Possible duplicate yet I still can't understand.)
Basic 2D revolving around origin:
...
0
votes
0answers
5 views
Finding Vectors in cartesian form [migrated]
I am stuck on this question could you please help me.
Find,in Cartesian form, the equations of the straight line through the point with position vector (-1,2,-3) parallel to the direction given by ...
2
votes
2answers
143 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
113 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
57 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
49 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
145 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 ...
0
votes
2answers
148 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
146 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 ...
3
votes
2answers
205 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 ...
3
votes
4answers
90 views
What is the inverse of CoefficientList?
I have numbers in vector notation. I need to get polynomial notation from them.
My numbers are {0, 1, 23, 5, 15, 0, 0, 0}. I want to get x + 23x^2 + 5x^3 + 15x^4 ...
2
votes
1answer
55 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
180 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
49 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
124 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
100 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 ...
6
votes
2answers
287 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
70 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 ...
0
votes
0answers
25 views
How to define a vector of arbitary length [duplicate]
I need to use a vector of length which I can change, indexed symbolically
So for e.g. when N=3 I'd like to have
vec={c1,c2,c3}
when N=5
...
2
votes
1answer
149 views
Directional derivative of SiegelTheta
I'm working on a problem where I have to integrate both the Mathematica function SiegelTheta and some of its second order directional derivatives. Using the function works well but something goes ...
0
votes
0answers
153 views
Plot a vector field, illustrating its continuity [closed]
I am trying to plot a Magnetic Field inside and outside of an accelerating tube.
While the solution is correct, when I try to plot I can't see the continuity on the edge of the cylinder.
My code is
...
3
votes
3answers
142 views
Multiply (not divide!) Vectors in a List by Their Own Norm
I wanted a set ("list") of 100 random vectors of dimension 2. I accomplished this already by generating a "list of lists" where the elements of the overall list are 2-dimensional lists consisting of 2 ...
3
votes
1answer
235 views
Plotting a complicated vector field
If we consider the vector $\left ( A \cdot \nabla \right) \: B$, we have in Cartesian coordinates
$$\left ( A \cdot \nabla \right) \: B = \left ( A \cdot \nabla B_x \right ) e_x + \left ( A \cdot ...
2
votes
1answer
423 views
Visualize eigenvectors at specified points?
I am very new to Mathematica and I got stuck about visualizing eigenvectors 2D and 3D.
I want to visualize my largest eigenvector field of tensor data(15x15). I wrote this code for instance :
...
3
votes
1answer
147 views
How can I independently move vector components (in 2D)?
Here's what may well be a simple problem that I have been having difficulty with:
There are two connected vectors, v1 and v2, such that:
v1 begins at the origin and and ends at point a1
v2 begins ...
3
votes
3answers
165 views
How to pull scalars out of a function that should act on lists?
Suppose I have
A = a vecA
B = b vecB
where a and b are supposed to be arbitrary scalars ...
4
votes
5answers
440 views
Vectors with a certain magnitude in Mathematica
For a user specified magnitude, is there a way to have Mathematica produce any 3D vector that fits that magnitude?
2
votes
0answers
152 views
VectorPlot scaling problems
When I plot a uniform field with zero values everywhere with the following command: VectorPlot[{y - y, x - x}, {x, -3, 3}, {y, -3, 3}]
the result are horizontal ...
2
votes
0answers
147 views
How to plot function & integral with vector variable?
I want to plot functions & integrals with vector variable the present in this paper.
For example the equation (5) at p. 3: I want to plot a chart like figure 5, i.e. the $x$-axis is the angle ...
1
vote
1answer
302 views
Plot 3D vector that is a function of one variable
I have a function, r[t], which is a piecewise function that generates a 3D vector. It looks like this:
...
3
votes
4answers
120 views
Pack Solve results into a vector
I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace:
...
1
vote
2answers
178 views
Symbolically associate vectors and their norms
I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like
...
2
votes
1answer
126 views
Orthogonalize method, keeping to binary vectors
The built in function:
Orthogonalize[m]
where m is a list of vectors returns a orthogonal basis for m. However, I want to stick to the binary field. However, I ...
1
vote
3answers
301 views
Span of a set of vectors over a given field
Could anyone help me find a function that takes as inputs:
a set $S$ of vectors and an integer $q$
and outputs:
the Span of $S$, where $Span[S]$ is a vector space over the field $F_q$.
If its ...
10
votes
0answers
560 views
Persistence length of a polymer chain
I'm trying to calculate the persistence length (Lp) of a polymer chain using Mathematica. The first and simplest method is to compare the EuclideanDistance between ...
2
votes
3answers
180 views
Force VectorPlot3D to show One arrow
I am plotting a curl, and I only want VectorPlot3D to show one arrow, I have tried adjusting VectorPoints-> 1, but the plot show's no arrows at all. Is 2 the minimum VectorPoints I can have?
If I ...
6
votes
2answers
419 views
Plotting a path in a vector field
I am trying to make a visual representation of the curve $y=x^{2}$, with $x\in\left[0,1\right]$ in the vector field defined by $\vec{F}=\left[-y,x\right]$.
However, as far as I can tell there does ...
3
votes
1answer
102 views
12
votes
4answers
305 views
How do you decompose a polynomial matrix into its matrix coefficients?
Let's say I have a matrix, $\mathbf{M}$, that is polynomially dependent on a single variable, such as
M = {{15 + a^2, a + 5 a^2}, {a - 5 a^2, 2}}
and I want to ...
8
votes
4answers
697 views
What is the cleanest way to prevent divide-by-zero warnings?
If I evaluate {1, 2, 3, 4}/{5, 6, 0, 8}, obviously I get one warning:
...
7
votes
2answers
398 views
Integration with vector coefficients
I asked this same question in Mathematics, and it was suggested I might try here. I'm more comfortable with Maple, but if I can get Mathematica to do what I'm after, so much the better.
Basically ...
27
votes
2answers
838 views
Animating a Voronoi Diagram
edit: Excellent answers have been provided and I made an animation which is suitable for my use, however, all the examples rely on bitmap/rasterized data; is there a vector based approach?
I would ...
14
votes
6answers
881 views
Why can't I define vector v as having subscripted elements v_1, v_2, v_3…?
I'm a very beginner in Mathematica 8 programming. While trying to play a little with tensor analysis I encountered a problem. How to define for example vector in such manner:
v={$v_1,v_2,v_3$}
For ...
4
votes
1answer
229 views
How to fix errors in Gram-Schmidt process when using random vectors?
I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
3
votes
2answers
571 views
creating vectors with normal distribution of lengths
First consider vectors of unit length, say on the unit sphere.
Now I want to give some magnitude to these vectors and I want the magnitude to be chosen from the normal distribution.
In one dimension ...
13
votes
2answers
745 views
How to represent and manipulate abstract indexed vector (or tensor) expressions?
I have a couple abstract indexed quantities, both differential elements
$dx = dx^\mu e_\mu + x^\mu de_\mu$
$du = du^\mu e_\mu + u^\mu de_\mu$
I can compute the expression $(dx + du) \cdot (dx + du) ...
