Mathematical vectors, operations on vectors and vectorized programming.

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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 $a,b \in \mathbb{R}^l$ ...
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1answer
165 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
103 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
87 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
201 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
70 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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52 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. ...
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1answer
535 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
234 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
64 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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254 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
198 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
117 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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2answers
225 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
299 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
85 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
104 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
63 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
51 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
180 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 ...
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2answers
113 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
89 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 ...
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1answer
134 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
126 views

Manahalobis distance between two vectors

I want to calculate the Mahalanobis distance between two vectors that represent two points. For example: ...
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2answers
192 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
52 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 ...
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1answer
735 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 ...
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1answer
339 views

Solving vector equations

I made this very simple module to try and solve vector X: ...
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2answers
188 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 ...
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1answer
125 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 ...
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96 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
129 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
110 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: ...
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2answers
131 views

How can I visualize an array of very small vectors spaced on very large grid? [duplicate]

I have data in the form points = {{1, 1, 1}, {1, 1, 2}, ...} vectors = {{2, 2, 5}, {2, 1, 7}, ...} Can somebody help to edit this data so I can ListVectorPlot a ...
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2answers
167 views

How to initialize several elements per iteration with Table?

I would like to initialize this kind of vector : {0,0,1,1,0,1,0,1,1,1,1,1} with Table. I tried ...
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2answers
123 views

Complex result for Real vectors in VectorAngle

I was expecting a real angle using VectorAngle when passing real valued vectors, however I obtained a complex angle. ...
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3answers
307 views

“NotAvailable” and “NotApplicable” data points returned by WeatherData[]

I am trying to use ListVectorPlot in combination with WeatherData and CountryData to show ...
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51 views

Multiply value if it includes a period

I download data from an online source, now I have a problem: the source code doesn't allow to differ between values of 10 (which actually stands for 10) and 10.000 (which is 10'000, but Mathematica ...
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1answer
148 views

Finding the maximum of a gradient vector

Im trying to find the maximum of my gradient vector G[x,y], I've tried several options including FindMaximumValue, FindMaximum etc. but i couldn't find it. The full function is shown below, any help ...
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50 views

Get rid of external library dependency

I am trying to generate C code for some functions, which I do not post in full because they are a few hundred lines long. The functions do nothing too fancy: a bunch of dot products, powers and roots. ...
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3answers
2k views

How to find the magnitude of a vector?

I'm doing this exercise in Wagner's book (p.78) , and this is my attempt: ...
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2answers
156 views

Is it possible to specify the direction of rotation in VectorAngle function?

If I use the function VectorAngle[{1,0},{1,-1}], is it possible to obtain the angle generated by rotating around the axis counter clock wise? In other words, I would move from the first vector to the ...
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2answers
202 views

Selecting parts of a matrix via indices given by a vector

I have a column vector of the form $\{1, 1, 2, 3, 2, 3\}^t$ and an associated matrix that has the same number of rows as the column vector, $6$, and a number of columns that is equal to the maximum of ...
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2answers
81 views
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1answer
229 views

Placing many arrowheads on curves

I can't find anything anywhere on the web to help me with this. My plot: ...
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131 views

Plotting Phase Space [duplicate]

I have these two Equ' $$x'[t]=Sin[y]$$ $$y'[t]=Cos[x]$$ and im trying to plot the phase space(plane) for this system... ive tryed Equationtrekker but cant seem to find the way to use it this way... ...
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2answers
143 views

how can I make a control for my vector equation in my simulation?

I'm trying to build a control selector or menu for equations to put into my curvature simulations. However all the code I've tried hasn't worked.Does anyone know how I could make a control selector or ...
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1answer
92 views

Simplification of linear algebra [duplicate]

I have a few vectors defined as V1 = Array[v1,3] V2 = Array[v2,3] V3 = Array[v3,3] And I am trying to solve a very simple equation along the lines of ...
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1answer
220 views

Show that three given vectors lie on a line, a plane, or span 3-space

Given three vectors, {2, 0, 0}, {0, 2, 2}, {2, 2, 3}, how could I see if they are all on the ...
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1answer
107 views

Plotting multiple vector fields with different domains in a single graph

I have attached a scheme of the problem. Essentially what I need is to plot 2 different vector fields in a single graph with different domains. The underlying physical problem is to model electric ...