Mathematical vectors, operations on vectors and vectorized programming.

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30 views

why Accumulate performs siginificantly different for two data sets with the same structure and length [on hold]

I used Accumulate to calculate partial sum for two lists of vectors. These two lists have the same dimension (same number of vectors, and each vector has three ...
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0answers
36 views

How to use the Mathematica to simplify a vector symbolic computation´╝č

I'm working with a rigidbody dynamic problem,and I have listed the "Newton-Euler" equation for a system.The equation I listed is very long and many items are included.I want to use the Mathematica to ...
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2answers
52 views

Vector optimization with vector length as a free variable

I'm trying to solve the following problem: For a vector $v$ of length $c$, $\min \frac{\sum v[i]^4}{(\sum v[i]^2)^2}$ subject to $\sum v[i] = N$. I can solve this numerically for a given $c$ using ...
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1answer
58 views

How to use DSolve with vectors without decomposing into vector components?

Given a basic, two-dimensional ballistic trajectory problem, I can solve the equations of motion using DSolve (or NDSolve) by ...
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1answer
43 views

Interpolate a discrete vector field

I have a discrete vector field, from which I want to derive the continuous one. For example, the planar vector field is defined by: ...
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42 views

ParametricPlot3D doesn't work with components of a vector input

I can't understand why ParametricPlot3D works, when the input is a vector and does not work, when the input is separated components of the vector (it returns an empty plot). The same happens for ...
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1answer
20 views

Inverse KroneckerProduct given other arguments

I'm having problems working out how to do the inverse of a two argument Kronecker Product, given one of the decomposed column vectors. For example, say I have used the Kronecker Product on two ...
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1answer
72 views

Phase Portrait Trajectories

How do I make a phase portrait which looks like the ones demonnstrated here? Not the fancy version where I can use the controls to change it, just a screen-shotted version of say a spiral point? Any ...
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0answers
17 views

How to find direction of velocity V2 to reach an object travelling at velocity V1, such that it takes least time? [migrated]

If an object A is currently at point P1 moving with constant velocity V1, and there is another object, object B which currently at point P2 which can move with velocity v2, then what should be the ...
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0answers
36 views

StreamPlot in 3 Dimensions

I would like to plot the vector equation $\left( {\begin{array}{*{20}{c}} {\frac{{ - a + \sqrt {{a^2} + 4bc} }}{c}}\\ {\frac{{ - a - \sqrt {{a^2} + 4bc} }}{c}}\\ 1 \end{array}} \right)$ as a stream ...
4
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1answer
97 views

How can I implement this recurrence equation in Mathematica?

I asked a similar question yesterday but today I realized that I was implementing the wrong function. I have tried changing the implementation but I can't get it to work. Problem: There is a river ...
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2answers
160 views

How can I express this recurrence function in Mathematica?

\begin{equation} r_{i+1}=r_{i}+V_{i}{\Delta}t \end{equation} Where \begin{equation} V_{i}=(0.01, 0.40) \end{equation} and ${\Delta}t$ is the difference in time. My implementation (this is for ...
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2answers
84 views

How do I do the Minkowski sum of two sets?

I have 2 sets, $X$ and $Y$. How do I find the Minkowski sum of these sets?
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2answers
60 views

Zero division in linear equation solution

I'm trying to transform a vector to another coordinate system with different root vectors. The other root vectors are defined by three points in space that form a plane, and it's a normal vector. ...
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1answer
66 views

Use ParametricNDSolve with Plotting

I am attempting to solve a differential equation of the form $$ \frac{dx}{dt}=ax+by \\ \frac{dy}{dt}=cx $$ with parameters $0<a<1$ and $a,b,c \in \mathbb{R}$. I am able to use NDParametric ...
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1answer
38 views

Vector Analysis in Version 8

Silly question. Why does Needs["VectorAnalysis`"] Grad[Sin[x^2 + y^2], {x, y}] give the error Coordinates::invalid: "{x,y} is not a valid coordinate system ...
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1answer
43 views

Plotting Vectors in Mathematic at lat/long positions

I have some current data that I want to plot in Mathematica. The first two columns are the latitude and longitude respectively (longitudes are negative b/c it is west of the prime meridian and all ...
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1answer
31 views

Protected Tag list and not a vector errors

I am working on a project for school, and I just need to find when the angle between a tangent vector and a line formed between two points. Here is the code I'm using: ...
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112 views

Solving Symbolically Equations with Vectors and Matrices

I want to solve equations with vector variables and vector/matrix parameters symbolically. As a basic example I would like to be able to solve something like $[I-aG]x=b$ where $a,b \in \mathbb{R}^l$ ...
5
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1answer
97 views

How to define an orthogonal basis in the right way?

I am trying to work with the vector notation without defining vector components explicitly. $Assumptions = (x | y | z) \[Element] Vectors[3] The vectors ...
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0answers
36 views

Problem with precision in ray tracing

today i was writing a ray tracer to find intersection point between a single ray and a cylinder. ...
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1answer
65 views

Mathematica error in vector element access

I have the following code, but Mathematica insists that xj is not a symbol! How may I fix that? ...
6
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4answers
167 views

Define Function with Sum over a list

I want to define a function that would symbolically look like $$ t(s,\underline{a})=\pi s + \sum_{n=1}^{n_{max}}a_n\sin(n \pi s) $$ (something like a finite Fourier series). Here $s\in [0,1]$ and ...
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37 views

How to solve a multi-vector optimization problem efficiently?

How to efficiently solve a optimization problem which involves multiple vectors? My optimization problem is: $\min_{\bf{K}_{i}} \sum_{i<j}\left[\bf{t}\cdot(\bf{K}_i-\bf{K}_j)\right]^2$, s.t. ...
2
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1answer
173 views

Inverse gradient operator

I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the ...
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2answers
195 views

VectorScale Explanation

I'm having great difficulty understanding VectorScale. Here are the definitions from the documentation. With the explicit specification ...
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1answer
59 views

Weird Vectorplot

I would like to Plot a simple Vector Field, all vectors normalized to one. If i for example take a evenly distributed sample of the field and plot it with the ListVectorPlot function, i get a plot ...
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0answers
97 views

Extract common factor from vector or matrix

I can't believe this hasn't been asked before but I can't find anything. Is there a way to convince Simplify or FullSimplify to ...
3
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1answer
145 views

Introduction to Vectors and NDSolve

I want to use NDSolve for a complicated equation that contains vectors. I am still new to Mathematica, and have really enjoyed what I have learned thus far. Concerning this question, I have already ...
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1answer
74 views

How to rotate vectors in vector plot?

I'm writing an exam for my calculus students and am seeking help with using Mathematica on a particular problem. Here's my idea: I want to give a multiple choice problem that has four choices of ...
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1answer
116 views

Simplifying symbolic expressions involving dot products

I have a function that outputs a large expression containing dot products of vectors. None of the vector components are known, so all dot products are symbolic. For instance, part of the output may ...
2
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1answer
191 views

How to control the length of vectors in VectorPlot

I want a slope field for a scalar differential equation. For simplicity I have chosen $dx/dt=rx$, where $r$ is a parameter. I used VectorPlot for the slope field as you can see from the code below. ...
2
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1answer
73 views

How can I use parts of lists with Dynamic?

I'm a newbie - what am I doing wrong? I want to use parts of lists (vectors) in calculations but Mathematica will not evaluate anything that involves parts of lists that update dynamically. Is there a ...
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2answers
90 views

Symbolic matrice or vectors in Mathematica?

Suppose I would like to define an expression, containing and array or matrix of symbolic elements. Like this ...
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1answer
52 views

Sort a vector of vectors of vectors

Let's hope I'm calling it well, I have this vector, or matrix, now I really don't know what it is ...
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2answers
47 views

Exporting mixed data of matrices and vectors / lists

thank you for reading my question. I have a problem trying to export mixed data from Mathematica. I have different matrices and vectors, which should be combined to a output file. Here a ...
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1answer
153 views

Basis for the intersection of vector spaces

The MuPAD Notebook Interface provides the linalg::intBasis function: http://www.mathworks.com/help/symbolic/mupad_ref/linalg-intbasis.html How can I get the same ...
2
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2answers
76 views

Returning the 3-dimensional vector from a skew symmetric matrix

I'm trying to write a function that takes in a skew symmetric matrix and returns the corresponding vector. When I write the following code, it works when I leave it as variables, but it does not work ...
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3answers
56 views

`Solve` with variables as single vector

Say I have a set of equations where the unknown variables are the elements of a vector $c=(c_1,c_2,\ldots)$ and want to solve it for $c$. Is there a way to do this with ...
3
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1answer
126 views

How to remove recursion, and write it functional and efficient way?

I wish to implement the following recursion efficiently. ...
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0answers
96 views

Manahalobis distance between two vectors

I want to calculate the Mahalanobis distance between two vectors that represent two points. For example: ...
3
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2answers
176 views

Simple Plot of Vector

I have a vector $<x(t),y(t),z(t)>$ constrained to a unit sphere. I am trying to plot what the vector looks like as time progresses. What would be the easiest approach to visualizing this? I ...
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1answer
47 views

Create vector for each vertex in a network [closed]

I have a network with x vertices and I would like to create a vector with random numbers for each vertex in this network. I would like to generate this list and represent it in a table. Further, it ...
2
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1answer
622 views

Plotting 3D Vector Field in one plane

I want to plot a vector field F={Fx, Fy, Fz}. However, I only want to plot it in one plane (say, z=0). When I use ...
2
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1answer
254 views

Solving vector equations

I made this very simple module to try and solve vector X: ...
3
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2answers
173 views

Orthogonal vector in two dimensions

Maybe this is really basic, but I couldn't figure it out. I would like to find the "hat vector" of a vector I defined: it's a vector orthogonal to the given one, assuming two dimensions. So for ...
2
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1answer
99 views

Changing the length of the vectors in vectorplot [duplicate]

I have the following code, and I've tried almost everything I can think of, even VectorColorFunction to describe magnitude. I am trying to make the length of the vectors proportional to r^{-2}, and ...
2
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0answers
91 views

Compile issues, scoping and order of evaluation

I have a few questions about compiling functions, which I think are all related to scoping and order of evaluation. I will illustrate them by a minimal example of the problem I have. I'm sorry for ...
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1answer
107 views

how to find the vector intersection in a collection of triangulated 3D points?

I'm trying to calculate the 3D point coordinates for the intersection of a vector with a plane. I have been using the following code to do this: ...
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1answer
85 views

Make 2D vector norm graph

I have: List of points on 2D plane: pointsz0 = ToExpression@Import@"http://pastebin.com/raw.php?i=VQfP0HgB"; And I have some values in those numbers: ...