Questions tagged [matrix]

Questions on the manipulation of matrices in Mathematica.

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5
votes
2answers
670 views

Loop and do operations on Matrix, then graph the results

I'm trying to do some operations to a matrix in a loop, and then I want to graph the results. The results are pair of numbers. Can I store the results of each iteration on "something" and the use ...
4
votes
2answers
996 views

Total Variation Distance of probability matrix

How can I calculate the Total Variation Distance of a transition Matrix? is there any built in function? I've searched all documentation and haven;t found anything. ** More information: Let me try ...
4
votes
2answers
537 views

Transform x-scale of data for e.g. MatrixPlot

I have to transform in a nonlinear way the x-scale of some data for a MatrixPlot (or ReliefImage or ...
2
votes
1answer
372 views

Numerical comparisons of matrices

I have a matrix which should be equal to a null matrix. However due to the numerical precision, a brutal equality test with a matrix initialized with zeros does not work. How should I perform the ...
4
votes
1answer
2k views

stationary distribution of a transition matrix

How can I solve the stationary distribution of a finite Markov Chain? In other words, how can I estimate the eigenvectors of a transition matrix?
10
votes
1answer
5k views

Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong?

If I ask Mathematica to find the eigenvectors and eigenvalues of the matrix: ...
3
votes
1answer
3k views

Creating a random normal matrix

I would like to create a random matrix with the constraint that the matrix must be normal, i.e. the matrix and its Hermitian conjugate must commute. I would create a random matrix "without constraints"...
12
votes
4answers
371 views

Inputting a big structured matrix in Mathematica

Hi this is my first post and this is a problem that has bothered me a lot. Suppose we have the $2012\times2012$ square matrix: $\begin{bmatrix}-3&1&1&1&1&1&\ldots&1&1&...
12
votes
1answer
1k views

How to extract and replace submatrix of a doubly-periodic matrix?

How can I effectively extract and replace a rectangular subpart of a toroidal matrix, i.e. one where boundaries are connected at opposite ends? Since the submatrix can overhang the edges, a simple <...
12
votes
2answers
568 views

How can I compute the representation matrices of a point group under given basis functions?

Take the $C_{3v}$ point group for example: ...
2
votes
3answers
2k views

Finding eigenvalues of a $1500\times1500$ matrix

I need to find the eigenvalues of a $1500\times1500$ real symmetric matrix given by $A_{i,i+1}= A_{i+1,i}=-1$ and also $A_{1,N=1500}=-1$ (this is because of a periodic boundary condition used) and all ...
11
votes
2answers
6k views

How to get MATLAB data imported with the same dimensions?

I have some MATLAB image data with the following dimensions (output is from MATLAB): >> size(im) ans = 86 86 3 45 The data imports just fine ...
6
votes
4answers
5k views

How to convert equation to vector (matrix) form?

How can I convert expression a1*u1+a2*u2+a3*u3 to the vector form of dot product A.U, where ...
1
vote
1answer
1k views

Is Mathematica matrix multiplication with its inverse wrong? [duplicate]

Possible Duplicate: Why don't * and ^ work as I expected on matrices? When I enter this ...
1
vote
2answers
3k views

How to Solve or LinearSolve $A = I$ matrix equation?

I'd like to solve this equation for $A = B$ where $B = I$, which represents 3 systems of 3 linear equations, for $a, b, c, d, e, f$, without writing LinearSolve 3 ...
16
votes
3answers
2k views

Mathematica for linear algebra course?

I'm taking a linear algebra / matrix theory course and we are free to use any software we want, and will be "expected to use MATLAB or an equivalent" for homework. The professor and textbook (Applied ...
3
votes
4answers
224 views

Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
14
votes
3answers
2k views

Correcting a correlation matrix to be positive semidefinite

Does Mathematica have a way to "fix" a correlation matrix that is not positive semi-definite? I looked through the documentation and search the internet but could not find anything.
6
votes
1answer
1k views

How to turn a random graph into a matrix

I have constructed a random graph with Mathematica using the RandomGraph command. Now I would like to convert this graph to a matrix, but I don't know how. The ...
4
votes
2answers
240 views

Standardizing a coset table via matrix manipulation

Suppose we have a group $G$ and a subgroup $H$. A coset table encodes the permutation representation of $G$ on the right cosets of $H$. When we want to use these coset tables in calculations, it is ...
7
votes
4answers
2k views

Swap two entries in a matrix

Is there a nice, simple script one can use to swap two entires in a matrix? For example, suppose we have the matrix below: $A=\begin{pmatrix}2 & 4 & 1\\ 3 & 1 & 2\\ 4 & 3 & 1 \...
1
vote
2answers
302 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 ...
1
vote
1answer
1k views

How do I use a matrix that has a variable?

I seem to be getting an error whenever I try running this piece of code. Matrix12[n_] := {{1, 0}, {0, {\[Kappa]1[n]}/{\[Kappa]2[n]}}} I've already defined the ...
6
votes
3answers
6k views

Passing a matrix as a function argument

I am trying to do the following: ...
6
votes
1answer
1k views

vectorial ODE in mathematica with matrix exponentials

I want to solve the following equation in mathematica : DSolve[{X'[t] == A.X[t], X[0] == ( {{0},{0}} )}, X[t], t] It is a system of 2 ODEs coupled by the matrix A, ...
3
votes
3answers
582 views

Can RowReduce work in this matrix?

The matrix $Q$ with dimensions $n\times2*n*m$ is structured by $$Q=[B|AB|\cdots|A^{2*n-1}B]$$ where $Q$ is an augmented matrix built from a $3\times3$ matrix, $A$, and a $3\times2$ matrix, $B$. I ...
9
votes
1answer
905 views

Efficiently Constructing Rank One Approximations for a Matrix using SVD

Suppose I have a $m\times n$ matrix $A$ (real for simplicity). Then SingularValueDecomposition[A] yields 3 matrices $U$, $\Sigma$ and $V$ such that $A = U\Sigma V^...
6
votes
1answer
1k views

Finding the characteristic polynomial of a matrix modulus n

Given a square matrix, is it possible to calculate its characteristic polynomial modulo n? Unfortunately, this function ...
8
votes
4answers
866 views

Prepend 0 to sublists

My question is similar to this one, but my goal is to prepend a single 0 the each sublist, not incrementally many 0's. The file I'm working is a CSV containing around 50K sublists of length 35. I've ...
4
votes
2answers
2k views

Matrix multiplication in Block Form symbolic calculation by Mathematica

I have a problem which requires taking product of two $10\times10$ matrices. I would like to do it by considering both matrices as $5\times5$ matrices such that each entry of both matrices is actually ...
26
votes
6answers
8k views

Best way to create symmetric matrices

From time to time I need to generate symmetric matrices with relatively expensive cost of element evaluation. Most frequently these are Gram matrices where elements are $L_2$ dot products. Here are ...
17
votes
5answers
1k views

Decomposing a matrix with polynomial elements into a polynomial with matrix coefficients

Let's say I have a matrix, $\mathbf{M}$, that is polynomially dependent on a single variable, such as M = {{15 + a^2, a + 5 a^2}, {a - 5 a^2, 2}} and I want to ...
4
votes
1answer
1k views

Computing Slater determinants

I need to compute Slater determinants. I'm wondering if I would benefit from assigning each of my functions to a variable prior to computation. I'm working with Slater determinants, but my question ...
4
votes
2answers
5k views

A dot appearing after a zero, and making the entries of a matrix into fractions

For more info about the difference between 0. and 0 I am a self-taught Mathematica user and I have some elementary questions-- perhaps too elementary for this site, but here they are. If you look ...
5
votes
1answer
3k views

exporting list of matrices in mathematica

I am working on some problem which requires generating a list of random matrices. So I used the code (actually a shortened version of the code, but it does not matter) ...
38
votes
3answers
2k views

Tiling a square

I wondered if there was a way to automate the process of finding a way to tile a tile into a square. The idea is to represent the tile with a matrix of $0$s for blank space and $1$s for filled spaces ...
3
votes
2answers
2k views

How to substitute numeric values in a symbolic Jacobian matrix?

I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
9
votes
3answers
444 views

How to extract and compute on the diagonal entities of a sparse matrix very fast?

As could be seen in the following code: ...
27
votes
1answer
5k views

Is there a way to convert an image into a Graph?

I'm trying to convert an image with several overlapping dots into a Graph. The goal is to be able to derive the Kirchhoff matrix for the randomly created "network ...
15
votes
3answers
688 views

Using uniform coloring in MatrixPlot

I have a rectangular matrix, which is m-by-10. Each element is either 0 or 1. I would like 0 to correspond to white elements, and 1 to red elements. This works ...
15
votes
1answer
15k views

Is it possible to substitute tick labels with alternative text? [duplicate]

Possible Duplicate: Labelling ArrayPlot Charts I am making a MatrixPlot. For example, consider the following: ...
7
votes
2answers
6k views

How do I keep the right ordering of eigenvalues using Eigensystem?

I'm having an issue with the Eigensystem command. I need to diagonalize a bunch of 3 by 3 complex valued matrices, but more importantly, I need to keep the exact ...
2
votes
1answer
225 views

Different determinants on 2 different computers

Is there any way to force Det to do itself in a certain way? I've been running the same notebook on 2 differents computer, one MacOSX Lion and one W7 (both 32bit) ...
7
votes
0answers
422 views

Inverse of a large sparse Hermitian block matrix

I am looking for a method (if it exists) for the inverse of a large sparse Hermitian block matrix. The off diagonal sparse matrices, named δ are 4x4, and they have ...
14
votes
3answers
2k views

Constructing a symbolic Hermitian matrix

I need to construct a symbolic Hermitian matrix like m = { { n, a, b, b}, {Conjugate[a], n, b, b}, ... } but I am not able to set ...
14
votes
2answers
3k views

Non-commutative symbolic linear algebra

I am fairly new to Mathematica but I thought I would be a helpful tool to carry out a few simple linear algebra calculations. It seems like an easy task but I cannot figure out how to do it. For ...
10
votes
1answer
2k views

Bordermatrix from $ \mathrm\LaTeX $

How would I create an output similar to the result produced by this $ \mathrm\LaTeX $ code: ...
4
votes
1answer
108 views

Trouble using FindInstance with MatrixRank

I'm really confused about what's going wrong with my call to FindInstance: ...
26
votes
2answers
2k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in Mathematica (which I found through this SO answer): essentially, I want to differentiate noisy data. ...
9
votes
3answers
2k views

Add lists with unequal lengths together to create a matrix

I'm trying to create a stacked bar chart using raw data coming from a MySQL server. The result coming back from one query is: ...