Mathematical vectors, operations on vectors and vectorized programming.

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3
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1answer
101 views

Finding the attractors of the vector field constructed as the gradient of an interpolated 3D scalar field

I have a list of data existing as {{{x, y, z}, f},...} from which I construct a 3D interpolation function using Interpolation[ ]. I am able to construct a vector field from the gradient of this scalar ...
4
votes
1answer
87 views

random distribution vectors on cube edges

How can I put randomly eight vectors with length b into eight edges of a cube with side of a and specify them with their ...
0
votes
1answer
120 views

How to plot the position vector r(t) = 3 cos(3.3πt)i + (sin(4πt) + 4t)j with t being a min of 0 and max of 1? [closed]

Every time I try using the ParametricPlot, nothing shows up. This is what i've done so far: ParametricPlot[{[3 cos[3.3 πt]], [sin[4 πt] + 4 t]}, {t, 0, 1},
4
votes
3answers
108 views

Find six vectors with rational entries under constraints?

Define six vectors v[i] with i=1,2,3...,6. Each v[i] is six dimensional and all entries in ...
1
vote
1answer
156 views

Linear Fit of multidimensional data

I am trying to find linear decomposition of vector B (of arbitrary dimension $n$) in the form : $B = \alpha_{1} C_{1} + \alpha_{2} C_{2} + ...$ where $C_{i}$ are known vectors (of dimension $n$) ...
14
votes
2answers
671 views

How to detect loops in a vector field?

Given a vector field and I'd like to detect if there are streamlines in closed patterns. For example, if the input is a vector field like this: ...
2
votes
3answers
93 views

Making a list of functions

Suppose I have the following equation system to solve: x(t_):={x1(t),x2(t)}; DSolve[x'(t)==x(t),x(t),t] This code works fine, but now suppose that instead of 2 ...
3
votes
2answers
104 views

Creating a tube with custom caps

I need a tube with only one end capped. I can do this relatively easily with: ...
0
votes
2answers
125 views

How does one define a function that takes vectors as arguments but also derivatives?

Summary: tldr; I just want to implement a version of the following mathematics function: $$ f(a) = c_1 e^{-(a - t_1)^2} + c_2 e^{-(a - t_2)^2} + c_3 e^{-(a - t_3)^2}$$ in mathematica, and be able ...
1
vote
0answers
53 views

Transform a vector DE into a set of scalar DEs [closed]

I have the vector equality: {{a,b},{c,d}}.D[{x1[t],x2[t]},t]=={{e,f},{g,h}}.{u1[t],u2[t]} I want to solve this using DSolve. ...
2
votes
1answer
74 views

Transforming an Optimization Problem into a multi-vector Optimization Problem

I am sitting on an MultiAgent optimization problem trying to solve for a quadruple of variables {e,l,b,c} In a single agent (...
5
votes
2answers
200 views

Is it possible that we can use “+” to add two vectors in polar form?

For example, $a=(2,\pi/4)$, $b=(3,\pi/3)$, if we want to get the result of $a+b$, using + operator will not do, because mathematica will ignore the polar form, and ...
0
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0answers
54 views
0
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1answer
58 views
0
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2answers
96 views

vectors constructed with $0,1$ permutation

Our desire is to construct $2^N$ vectors with indices $i=1,..,2^N$ with elements by permutation of $0$ and $1$. For example ($N=3$): We write below code ...
0
votes
1answer
55 views

Designing a loop that fetches 5 random vectors each with 5 components from a set of 10 until Linear dependence is found

I am currently trying to find a way to make a loop that will select 5 random columns without replacement of a 5x10 matrix until it finds a determinant equal to 0 out of the new matrix formed by the 5 ...
0
votes
0answers
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: ...
1
vote
1answer
73 views

Singularity Messing up Scale in Vector Field

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4
votes
1answer
119 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 ...
0
votes
0answers
26 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, ...
8
votes
2answers
862 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 ...
0
votes
1answer
62 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 ...
3
votes
2answers
464 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?
0
votes
0answers
79 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} ...
3
votes
2answers
135 views

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

I'm using code like this: ...
1
vote
1answer
173 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 ...
1
vote
1answer
242 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 ...
0
votes
2answers
100 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 ...
2
votes
3answers
80 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 ...
1
vote
2answers
96 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. ...
3
votes
1answer
144 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: ...
0
votes
0answers
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
votes
2answers
217 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: ...
-1
votes
1answer
112 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.
-3
votes
1answer
90 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." ...
1
vote
3answers
66 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 ...
0
votes
2answers
78 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 ...
5
votes
1answer
182 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 ...
2
votes
1answer
217 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: ...
1
vote
1answer
39 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 ...
0
votes
1answer
137 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 ...
1
vote
0answers
102 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
votes
1answer
149 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 ...
2
votes
2answers
215 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 ...
1
vote
2answers
265 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?
0
votes
2answers
89 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. ...
0
votes
1answer
247 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 ...
0
votes
1answer
68 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 ...
2
votes
1answer
65 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 ...