Mathematical vectors, operations on vectors and vectorized programming.

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n dimension vector expression in mathematica

I have a question about how to write the formula in Mathematica. If $w$ is $n$-dimensional vector, with each element as $w_i : i=1,2,3,...n$ and $n$ is symbol, how to write it as vector in ...
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1answer
40 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 ...
2
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2answers
205 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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21 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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86 views
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1answer
61 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
64 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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2answers
58 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
61 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
69 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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28 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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24 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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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 ...
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2answers
166 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
54 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
53 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
39 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
55 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
78 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
55 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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53 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
26 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
81 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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39 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
113 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
174 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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96 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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67 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
86 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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40 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
50 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
40 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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172 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 $a,b \in \mathbb{R}^l$ ...
6
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1answer
119 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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43 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
74 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
178 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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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. ...
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1answer
328 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
208 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
60 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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168 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 ...
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1answer
158 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
82 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
169 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 ...
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1answer
234 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. ...
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1answer
80 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
97 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
56 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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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 ...