Mathematical vectors, operations on vectors and vectorized programming.

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38 views

How to solve a system of equations which includes vectors? [duplicate]

I'm starting to wonder if this is something that mathematica just can't do? I thought something like this might work: ...
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1answer
67 views

Singularity Messing up Scale in Vector Field

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4
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1answer
101 views

Superimposing ListLineIntegralConvolutionPlot with transparent noise over ListContourPlot

I have an array of 128x256 data points in a rectilinear array. For each point there is a 2D vector quantity and a scalar quantity (normalised to -1 <= x <= 1). I very much like the ...
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23 views

PolynomialGCD in complex numbers for vector simplification

I wanted to define a function $f(t,\vec{r})=e^{i\omega t-i\vec{k}\cdot\vec{r}}$, and take gradient of it. With, ...
7
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2answers
628 views

Defining quantum-mechanical Bra and Ket operations

I have the following ket in the Fock basis: $\vert3, 0 ,1\rangle$, where each entry defines the number of photons in a particular mode and can take any one of the following numbers: 0, 1, 2, 3. As a ...
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1answer
60 views

Beginner: Iterative Sequence for Vector Function

I want to create an iterative sequence for two Vectorfunctions, where both are dependent on the same variables and i represents the vector. For simplicity let's ...
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2answers
342 views

How to make Mathematica show matrices and vectors nicely

It shows me like {{0}, {1}, {0}, {-1}} . Is it possible to make it look like a vector, always?
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0answers
58 views

Working with vector-valued functions to solve an ODE

Let's say I have a simple vector-valued ODE given by $y'(t) = K*y(t)$ where K is a matrix $K_{n_{X}n}$. Let's assume that the matrix is $K_{21_{X}21}$, $K = \left[\begin{array}{cccc} k_{1_{X}1} ...
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126 views

How to extract state vector after NDSolve for subsequent re-use?

I'm using code like this: ...
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1answer
127 views

Divide each element of a list of 500 matrices by another matrix

Lets say that I have a Table of dimension (3,3,500) and I'd like to perform element-wise division by a 3x3 matrix along the third dimension (of length 500 in this case). What is the most elegant way ...
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1answer
187 views

Plot a numerical integration as a function of a variable

Suppose we have a function that is hard to evaluate analytically but a numerical estimate suffices. For example consider the $f(x,\Lambda) = \Lambda\cdot \sin(x)$ where $\Lambda$ is some parameter I ...
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93 views

Plotting vectors using derivatives

This question stems from a previous question I asked here: Multiple Integral of equation including dx prime? An equation describing a gravitational field of a cuboid is given as: $V(X,Y,Z) = -G\rho ...
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3answers
75 views

Referring to the components of a vector within a sum

I feel like I'm missing something obvious here, but.... I'm playing around, trying to do the standard deviation for my stats homework (don't worry, I already worked out the answer by hand), and I ...
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2answers
86 views

Problem in matrix multiplication

I created a random directed acyclic graph using Mathematica. I need to compute a specific function from its adjacency matrix. ...
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0answers
87 views

Controlling scaling of multiple vector fields in VectorPlot3D

I'm trying to plot the electric and magnetic fields of a relativistically moving electric charge using VectorPlot3D, and apply "Manipulate" to change the velocity. The code I'm using is as follows: ...
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128 views

Find the point of intersection of A,B,C-plane and D1D2-line

The problem. Five points A,B,C,D1 and D2 in R3 are given. (1) Determine whether three points A,B,C are collinear(i.e. lie on the same line). (2) If A,B,C are not collinear, find the plane that ...
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26 views

How do I get Mathematica to evaluate symbolic linear algebra [duplicate]

First of all, I am VERY new to Mathematica. That said...I have defined vectors as: e1=2x-y and e2=x+y (x and y are orthonormal). I also defined the dot products of x and y in Mathematica. I want to ...
3
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2answers
207 views

Vector Plot of a linearly varying cantilever

I want to drawing with Vector Plot a deflection and slope of a linearly varying cantilever. And with Contour Plot it works but with Vector Plot it didn't. Here is the code: ...
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1answer
103 views

ParametricPlot3D won't show [closed]

I want to see the image of a tube made from a space curve. I define the surface using Frenet-Serret frame but the software does not show me the plot. What might be wrong with my code? Thank you.
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1answer
74 views

Error in cross product [closed]

I want to take the cross product of two rather complicated vectors but Mathematica gives me error: Here is the input: The error I get is "The expression pu cannot be used as a part specification." ...
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3answers
56 views

Define a function of a vector without fully specifying the components of the vector [duplicate]

I have a vector $A=\{1,2,3,4,5,6\}$, and I want to define a function of $A$ as f[A_]:=A.X where $X$ is another vector. I want to define this function without ...
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2answers
76 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
155 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
164 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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1answer
36 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
117 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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70 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 ...
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1answer
143 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
208 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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212 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
88 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
205 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
56 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
62 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
60 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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0answers
401 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 $a,b \in \mathbb{R}^l$ ...
8
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1answer
233 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
120 views

Ray tracing: Insufficient precision

I am writing a ray tracer to find the intersection point between a single ray and a cylinder. ...
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1answer
112 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? ...
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4answers
246 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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1answer
85 views

Cannot shade 3D vector in different color

I need to color each vector into different colors... but this formula just doesn't work: ...
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2answers
310 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
70 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
486 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
253 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
175 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
313 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 ...
3
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1answer
442 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
112 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
128 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 ...