Questions on the manipulation of matrices in Mathematica.

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9
votes
4answers
277 views

Finding the position of similar elements in a matrix

I want to find the position of the elements which are equal in a matrix. For example in the case of the following matrix: $m =\left( \begin{array}{cc} a & x \\ x & a \\ \end{array} \right)$ ...
10
votes
5answers
1k views

Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...
18
votes
5answers
714 views

Graph from binary matrix (not adjacency) respecting the original matrix positions

I have a binary matrix. My objective is to connect every close (without "jump") elements with value equal to 1, but I must keep the point positions, just like it's shown at the image. Can somebody ...
2
votes
2answers
344 views

Create a matrix of matrices using Band and ArrayFlatten [duplicate]

I can easily write a simple Band matrix using: SparseArray[{Band[{2, 1}] -> a}, {Dim, Dim}] where a is a number. Now, I ...
1
vote
2answers
165 views

dropping a row with at least one value larger than a particular value

So for instance I have M X N table. I want to drop any row which has an element larger than, say, one in the second or the third column. I guess I have to do some sort of pattern matching. But not ...
2
votes
1answer
52 views

Complement for a Matrix

In a matrix, there are some non-zero elements same as: aA= Also, there is a list such as: list = {a, b, c, d, e, f, g, ii, jj, kk}; I want to access to ...
4
votes
3answers
395 views

Efficient matrix / array generation

What is the most efficient way of generating the following matrix? $\left( \begin{array}{ccccc} 1 & 0 & 1 & 0 & 1 & 0 & 1 & \dots\\ \frac{1}{2} & \frac{1}{2} & 0 ...
1
vote
1answer
120 views

Matrix/tensor addition behaving funny under replacement?

I have two matrices I want to add, and one of the matrices is a tensor product of two vectors. I've used a SetDelayed to define the summed matrix, because I want to evaluate it for different values of ...
0
votes
2answers
149 views

Improving code for comparing and modifying nested matrices

I have a matrix such as: ...
0
votes
1answer
52 views

Importing a Matrix whit different column numbers depending on the row

I have a bunch of coordinates given in a file. The file contains Startpoints and Endpoints of arrows in columns(Example): ...
3
votes
6answers
345 views

How can I construct a distance table?

I have a list of city names (of arbitrary length), f.e. c = {"BAL", "NYC", "LAS", "AUS"}; and the distances between them : ...
1
vote
3answers
191 views

Working with nested matrices

I have a matrix: A = {{a, b}, {c, d}} But each its element, itself, is another matrix too. ...
1
vote
0answers
102 views

How to find matrix exponential using RootSum? [duplicate]

From what I've been able to deduce, Mathematica uses a root sum scheme to determine the exponential of a matrix. Can someone please explain to me the theory behind this? I've searched, but have had no ...
1
vote
1answer
146 views

Matrix and random, weighted assignment of rows

I asked a question in this category previously but my problem has changed. On one hand, I have a large number of data files as .dat format, and on the other hand, I have a matrix ...
1
vote
1answer
50 views

Correctly substituting a matrix into a scalar equation [duplicate]

I am having trouble correctly substituting a matrix into an (originally) scalar equation. For example: A = {{3, 1}, {1, 2}} cp = CharacteristicPolynomial[A, x] ...
1
vote
1answer
163 views

Calculate the algebraic multiplicity of known eigenvalues of a large, sparse matrix

I have a large (and sparse) matrix with size 1000x1000 -- 10000x10000. I believe i know all eigenvalues for the matrices. All entries are integers and so are the eigenvalues. I want to check this by ...
1
vote
1answer
45 views

Evaluation of m.v is blocked by applying MatrixForm. Why? [duplicate]

I'm trying to understand what is happening in the notebook session below. I have a 2x2 matrix m = {{-1,-1}, {-1,-1}}. And a vector ...
2
votes
2answers
320 views

Convert DelaunayTriangulation-> Graph->AdjacencyMatrix

Is there a way to convert a Delaunay Triangulation into a Graph structure so that one can generate an AdjacenyMatrix of the Delaunay?
1
vote
1answer
109 views

Matrix and string variable

There are $100$ .dat data files which contain numerical parameters. ...
4
votes
2answers
133 views

Checking powers of a matrix for zeros

I'm currently working on a project that deals with numerical semigroups and their connection to matrices. I'm pretty new to Mathematica, so I wouldn't be surprised if my question has a simple ...
2
votes
1answer
70 views

Sorting a matrix except its last row

Given M = {{"Utah", 2}, {"Iowa", 1}, {"Maine", 3}, {"Total", 6}} I want to obtain the reverse-sorted result like this: ...
2
votes
2answers
171 views

Building adjacency matrix from set data

I have two sets: games and players. Players pick their games. As such I will have data say g1={p1,p3,p5},g2={p2,p4},g3={p2,p3,p5}. My interest though is to build the connections among players because ...
2
votes
1answer
187 views

Loop in solving multiple matrix calculation

I am wondering is there a way to use loop, like Do, For, to rewrite the last line in the code. I tried to use ...
0
votes
1answer
143 views

Select positive value from a vector

I am wondering how to pick out the positive Omega value from soln, and make these positive values into a row vector. I know how ...
0
votes
1answer
235 views

Factor vector out of a matrix

I am wondering how to factor a[1],a[2],...,a[4] out of sim so that I can write sim as the ...
0
votes
1answer
185 views

Mapping a function over n levels

I want to map a function over a matrix of rank n, for example: ...
1
vote
2answers
120 views

How to drop the identical rows and columns of a matrix?

I'm currently trying to find a way to eliminate from a square matrix of generic dimension the duplicate (up to sign) rows and columns, obtaining a smaller dimensional matrix. I searched around here ...
6
votes
2answers
264 views

Matrix exponential via Cayley-Hamilton Theorem

I'm attempting to calculate the exponential of a matrix via Cayley-Hamilton theorem. (Following the "concrete example" from http://en.wikipedia.org/wiki/Cayley%E2%80%93Hamilton_theorem) I am having ...
0
votes
2answers
137 views

Make an effective projection of matrix

To best explain my problem, I will take the following example: Consider the following matrix : ...
1
vote
3answers
101 views

Finding if a matrix is square

I have a matrix which is constructed element by element through some iterations, and thus can be non-square. If it's not square, then I want to make it square filling with ...
2
votes
0answers
113 views

A math function similar to “LatticeReduce” for finding linear independent basis

We would like to ask a math function similar to "LatticeReduce" for finding linear independent basis. The input is a list of vectors $M=\{v_1,v_2,v_3,\dots\}$, with the following property: There is a ...
2
votes
1answer
262 views

How to define a matrix with all elements 0? [closed]

A matrix can be defined as M = Array[m, {3, 3}] which gives ...
2
votes
1answer
152 views

Find positions where two matrices differ

I have two matrices A and B of identical dimensions. What's the simplest (shortest) way to find the indices of differing ...
2
votes
1answer
423 views

Matrix exponential MatrixExp[] vs Sum[MatrixPower[]] doesn't match?

I might be an idiot, but I cannot get the manual expansion of $e^{At}$ to match the MatrixExp[A t] result. For example, I have the following: ...
1
vote
1answer
115 views

Importing adjacency matrix from file of 0/1 arrays

Is it possible to import adjacency matrix for graph representation, from simple text file with NxN (rows x columns) of 0s/1s: 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0
3
votes
1answer
241 views

Are there any more time-efficient ways to solve a matrix equation than with SparseArray and LinearSolve?

I am trying to solve a matrix equation, with the matrix being tridiagonal. The problem I am having is that a message keeps appearing that I don't have enough memory. Here is the code: ...
6
votes
2answers
510 views

Combining three R, G, B matrices into a single matrix of 3-tuples?

Working with Mathematica 8 on OSX here. I have three $1024 \times 1024$ matrices representing the counts from consecutive exposures onto a CCD with $R$, $G$, and $B$ filters on it, and am looking to ...
0
votes
1answer
68 views

Show List of HighlightGraph Objects in Matrix

I'm new to Mathematica and can't get my problem solved. I want to display a list of HighlightGraph objects in MatrixForm like ...
2
votes
1answer
169 views

Multiple swapping of rows and columns

m={{a, b, c, p}, {d, e, f, x}, {g, h, k, z}, {u, v, w, y}}; I want to swap 1st and 2nd rows by 4th and 3rd rows respectively. And then, swap 1st and 2nd columns ...
3
votes
1answer
304 views

Plotting with ColorFunction -> GrayLevel - no black

This is probably a fairly trivial question, yet I have been unable to find an answer - help would be much appreciated! :) I am trying to plot a 28 x 28 matrix (tabulated data given here), containing ...
0
votes
0answers
63 views

TableDirection in TableForm

I got confused about what does "the outermost dimension" and "the first dimension" mean in the document I snipped. Does it mean row or column?
0
votes
1answer
99 views

Matrix Operation

I have a $3\times3$ matrix A, and a function sTrans that outputs two $3\times3$ matrices in a list when given a $3\times3$ ...
1
vote
0answers
99 views

Find the values of parameters so that the matrix is symmetric positive definite

Good evening , I have a matrix 20x20 in symbolic form. The matrix depends on 5 parameters (a,b,c,d,e). I would like to get the interval of each parameters that ensures that the matrix S is symmetric ...
1
vote
2answers
155 views

How to sort the adjecency matrix of bipartite graph so to have two off-diagonal blocks

In a bipartite graphs there are two class of nodes, say A and B. Each node of class A may interact only with nodes of the class B, and viceversa. The corresponding adjecency matrix is thus composed by ...
4
votes
3answers
390 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
8
votes
3answers
657 views

Visualization of matrix transformations

I define the "matrix transformation" here as follows: $\left[ \begin{matrix} x_1' \\ x_2' \\ \end{matrix} \right]=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} ...
1
vote
0answers
45 views

How to get integer/rational and real eigenvectors to be the same? [duplicate]

forgive me if I missed this already being answered or too easy. Given a matrix: q = {{1, 3, 5}, {7, 11, 13}, {1/3, 1/7, 1/13}}; Eigenvectors are different here: ...
0
votes
1answer
304 views

How to get more accurate orthonormal eigenvectors?

I have a matrix M with real entries in MachinePrecision. I compute its eigenvectors and construct matrix ...
0
votes
0answers
62 views

How to compute variances from a matrix/table

I have created a matrix/table with an imported dataset. I want to know what the variance is for 3 values at a time but across 68 columns. I would like to do this in an automated way rather than 1 set ...
1
vote
0answers
70 views

Mathematica program for PLUR decomposition of a symbolic matrix using full pivoting

I wanted to ask if there is a Mathematica program for PLUR decomposition of a symbolic matrix M, such that M = P*L*U*R, using FULL (row and column) pivoting, and where R = reduced row echelon form of ...