Mathematical vectors, operations on vectors and vectorized programming.

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564 views

Span of a set of vectors over a given field

Could anyone help me find a function that takes as inputs: a set $S$ of vectors and an integer $q$ and outputs: the Span of $S$, where $Span[S]$ is a vector space over the field $F_q$. If its ...
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2answers
48 views

Computing symbolic norm of a vector

Consider the code: n1 := Cos[α] Sin[β] n2 := Sin[α] Sin[β] n3 := Cos[β] n := {n1, n2, n3} Norm[n] Why the result is ...
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2answers
292 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in ...
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2answers
257 views

Doing vector manipulations on Mathematica

This is hopefully a simpler version of this previous unanswered question of mine. Let me just focus on the two expressions $F_2^{(s)}$ and $F_3^{(s)}$ given in A.3 and A.4 of page 19 of this paper. ...
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1answer
244 views

Making a ListVectorPlot3D from data in an external file

I have a .dat file with six columns: {x y z vx vy vz}, where x, y, z are space coordinates and vx, vy, vz are the vector components. How can I use this file to get ...
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2answers
216 views

Symbolically associate vectors and their norms

I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like ...
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1answer
56 views

Partitioning a list and gathering statistics on the distribution of values across partitions

I have a one-dimensional array of 200 elements consisting of the numbers 0, 1, 2. This array needs to be divided into 10 groups (20 items each). Then, for each group, I want to count how many of the ...
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2answers
57 views

How do I avoid vector variables being treated as scalars in the course of replacements?

I often work with a mixture of symbolic and concrete values as I develop teaching materials. I introduce variables symbolically and then need to instantiate them to specific values while continuing ...
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1answer
110 views

Using Select on list of vectors [duplicate]

I have a dataset, where each element in the list is a vector as in data = Table[{i, 2 i, 3 i}, {i, 1, 10}] As an example, I am interested in the entries where ...
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1answer
106 views

Splitting list of sums into a sum of lists

I want to split a list of sums into a sum of lists For example, I'd like to turn {{x + y + z}, {x}, {y}, {z}} into ...
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4answers
213 views

converting between forms - symbols/subscripts - matrix products

If I have a vector of the form (xp+y, x+yp) do you have a simple way of creating the following matrix and vector from it: {{p, 1}, {1, p}} * {x, y}, such that ...
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1answer
126 views

Linear interpolation between defined anchorpoints in an array (where anchorpoints are set each time we see a new element)

This question is an update and a correction my earlier question: Linear interpolation of a list between periodic anchorpoints (which was nicely answered). Imagine I have a list of the form: ...
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1answer
122 views

Difference between vector's Dimensions

What's the difference between projection= Table[Conjugate[autoVett[[k]].someVector1], {k, 1, r}] Dimensions[projection] that gave me as results ...
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1answer
85 views

How to fix the number and length of vectors when using ListVectorPLot

I want to plot only the vectors that I specify in my list of vectors, and no more. ListVectorPlot plots many of them, namely plots the field extrapolating from my four vectors.I would also like to ...
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1answer
45 views

Operator operation

There are two basic operators r={x,y,z} and p=-I*h*{D[#,x] , D[#,y], D[#,z]} &. The angular momentum operator is defined as ...
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1answer
137 views

Need assistance with plotting Cell Center Points and Normals (ListPlot, ListVectorPlot)

This is the CellCenter datapoints and associated Normals data: http://wikisend.com/download/458974/CellCenters-and-Normals.dat The dat file contains data points for x,y coordinates and x,y ...
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0answers
86 views

Solving for vector elements in a function to which the vectors are not passed explicitly

I want to define a function which takes in two integers (indicating the lengths of 2 vectors), and solves a simple set of expressions at a set of points to find all the values in both the vectors. so ...
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1answer
250 views

How to define a fixed length vector in Mathematica?

I would like to define a 3-D vector as say v={x,y,z}, but I want it to have a fixed norm, say a unit norm |v|=1. How do I impose this condition on v.
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2answers
146 views

Apply a function to a matrix of vectors [closed]

I have a matrix containing on each position a pair of numbers $(a,b)$. I would like to compute the norm of each vector $(a,b)$ and keep the result in form of a matrix. So basically, I need to apply ...
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2answers
320 views

How to plot vector function r(t) = i + j + t*k

How can I plot the vector function $r(t) = i + j + t\;k$, where i, j, k are unit vectors, and t is the parameter of the function r.
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1answer
520 views

Plot 3D vector that is a function of one variable

I have a function, r[t], which is a piecewise function that generates a 3D vector. It looks like this: ...
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1answer
45 views

Factor a Vector

Does there exist a function in Mathematica that simply takes out a common factor from a vector/list of expressions? This seems like such a simple operation that I am surprised that I could not find it ...
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1answer
82 views

replace is not happening for specific vector valued expression

Given x[t_] := {Subscript[x, 1][t], Subscript[x, 2][t]} following replace works fine x[t] /. x[t] -> 0 0 but following ...
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1answer
91 views

How can I impose a condition on Solve or FullSimplify?

I would like to define a real 3-D vector as, say, v = {x, y, z}, but I want it to have a fixed norm and not necessarily a unit norm. I would like to impose this ...
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1answer
109 views

Symbolic matrix simplification and solving

I am trying to expand or solve an equation that contains matrices for a certain matrix, but it is not working: ...
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1answer
86 views

Rotating a set of 3D points against an arbitrary axis

I want to rotate a list of 3D points around unit vector (1,0,1) by the angle of Pi. How can I accomplish it?
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2answers
147 views

Plotting problem

I was wondering why I keep receiving the error message "Derivative should be a triple of numbers, or scaled form" from the following code ...
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1answer
194 views

Simplify vector expression - is there something like “Factor” for vectors, dot products etc.?

I am looking for a way to simplify dot products etc. Here is a minimal example: Lets say I have two vectors a and b: Array[a,2] Array[b,2] Now I evaluate their ...
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1answer
41 views

Function output of two lists are only diagonal elements

I'm having a little crysis over here. What I basically want to do is some sort of 3D-Plot, but I'm only interested in the resulting values. I have two vectors x and p: ...
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1answer
269 views

Circular Orbit Velocity in Vector Components

I'm trying to find out how to calculate the initial velocity needed to keep a spacecraft in a circular orbit around the Earth given its initial position and an initial angle theta in a Cartesian ...
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2answers
341 views

How to input a 3-vector in spherical coordinates?

I would like to input a 3-vectors in spherical coordinates $(r, \theta, \phi)$ and be able to operate on such vectors (dot and cross product) with the results being given in the same spherical ...
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1answer
93 views

Setting Variables Inside VectorPlot3D [closed]

I was trying to plot a vectorfield of a gravitational field. I was wondering if there's any way you can set $R = \sqrt{(x-3)^2+(y-3)^2+(z-3)^2}$ Inside the command: VectorPlot3D[{-((x - 3)/R), -(y ...
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1answer
80 views

Vector-calculus [duplicate]

I have a table of 200 elements, elements are '0', '1', '2'. I have participate them into groups for 20 elements each one. Then I have calculate how many '0', '1', '2' are in each part. And then in ...
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1answer
56 views

Extract random points from a 3D manifold [closed]

Could anyone help me with this problem? I have a 3D manifold given by $$1<d<b<c,\;\;b+d<c,\;\;b+2d>c.$$ My goal is to find a lot of points belong to it.
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28 views

Is it possible to obtain vector differentiation results in terms of vectors rather than components? [duplicate]

When doing certain operations on vectors in Mathematica it is quite desirable to convert the results back into coordinate-free notation. Unfortunately, after going through the Documentation Center and ...
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0answers
80 views

Visualizing 3D vector field on surface of sphere [duplicate]

I want to vizualize (quite complicated) 3D vector field which has both real and imaginary part and is expressed in spherical coordinates. I was thinking about expressing the field for certain r and ...
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0answers
33 views

Using Manipulate, how do you display the points on the curve and the tangent vector? [duplicate]

I'm new to Mathematica and my assignment is very vague... I'm hoping someone can explain to me a bit more of that this quesion means: Given the curve C, display the point on the curve and the ...
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0answers
82 views

Gradient from Vectors type

I'm working with Vectors type in Mathematica 9. For this purpose I use the following command: ...
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0answers
100 views

Simplify function with normalized vector

I made a very simple case: testF[x_, y_, z_] = x^2 + y^2 + z^2 Simplify[testF[x, y, z]] If {x, y, z} is normalized, the simplified result should just be 1. How ...
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0answers
114 views

Any way to fully expand an expression of two operators?

I am looking for a way to expand a complicate expression like the follow (A o B + C o (DxE))*(D o (ExF) - ExA + A) Here o and x are the operator. I want to ...
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0answers
29 views

How to define a vector of arbitary length [duplicate]

I need to use a vector of length which I can change, indexed symbolically So for e.g. when N=3 I'd like to have vec={c1,c2,c3} when N=5 ...