Questions on the manipulation of matrices in Mathematica.

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2
votes
2answers
126 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 ...
2
votes
0answers
93 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 ...
1
vote
3answers
94 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 ...
0
votes
0answers
43 views

Extracting Coefficient Matrices from partial differential equations

I have a system of differential equations which are in the form Dt[a01,t] + u*Dt[a01,x] + v*Dt[a01,y] + w*Dt[a01,z] I have ten of these equations and my ...
2
votes
1answer
89 views

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

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

Package for representation of groups (group theory)

I wanted to know if there is a package which allows to compute representations of a group like the definition representation, adjoint and so on (for example the Pauli matrix for $SU(2)$ if I specify ...
2
votes
1answer
134 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 ...
1
vote
1answer
57 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
130 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: ...
5
votes
2answers
318 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
64 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
132 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
115 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 ...
4
votes
3answers
274 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 ...
0
votes
1answer
286 views

How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
0
votes
0answers
43 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?
3
votes
2answers
99 views

How do we make a negative integer out of a string of a negative number and vice-versa?

Negative numbers are not taken into consideration by mathematica's built-in functions. FromDigits["-2"] Gives me this message: ...
0
votes
0answers
42 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
94 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 ...
0
votes
0answers
43 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
110 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
57 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 ...
0
votes
1answer
190 views

Symbolic Jacobian computation

I have an equation for which I would like to compute the Jacobian symbolically. $$f(x)=Ax-diag(x)(Ax+b)$$, where $x\in \mathbb{R}^n$, $A\in \mathbb{R}^{n\times n}$ and $b\in \mathbb{R}^n$. I am new ...
57
votes
7answers
11k views

Elegant operations on matrix rows and columns

Question The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a ...
0
votes
0answers
59 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
0
votes
0answers
24 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 ...
1
vote
1answer
45 views

Formatting All Appropriate Output as Desired Automatically

I want to output in MatrixForm whenever I have a list/vector/matrix, but I do not want to have to type out the command each time. How can I write one command at ...
0
votes
2answers
149 views

Taking averages at certain intervals

I am trying to take averages of a large two dimensional array at certain intervals. For example, for the first row, I want to take K averages of 500 values. Here is what I am trying ...
0
votes
2answers
117 views

setting real parameters in Hamiltonian matrix

The following Matrix represents my Hamiltonian. m = {{ B/2 - d - j/2 + a, (Sqrt[2]*j)/2, M}, {(Sqrt[2]*j)/2, B/2 + a, 0}, {M, 0, (-3*B)/2 - d + j/2 + a} How can ...
1
vote
1answer
84 views

Mathematica does not respect tensor order?

I'm trying to verify an identity involving symmetric traceless tensors over the reals. What I tried was: ...
0
votes
1answer
33 views

Generate array of every $n^{th}$ integer between two bounds [closed]

I want to generate the series {1930, 1934, 1938, ..., 2014} with Mathematica. I found that I can use Sum[2014-m*4, {m, 20}] to ...
6
votes
1answer
168 views

Symbolic scalar-by-matrix derivative

Let's say I want to calculate the following scalar-by-matrix derivative $$\frac{\partial}{\partial A} \text{tr} \left[(\vec X^T A)^T (\vec X^T A)\right],$$ with $\vec X$ and $A$ being a $n \times 1$ ...
2
votes
2answers
248 views

Covariance of a P x M x N matrix

I have a stack of tiff files. When imported to Mathematica, they form a $P \times M \times N$ matrix, where $P$ is the number of single images in the stack, $M$ is the number of horizontal pixels and ...
0
votes
1answer
115 views

Determinant of a square matrix with univariate polynomial entries is not a polynom? [closed]

I have a 15x15 Matrix with all polynomial entries. I want to calculate the determinant of the matrix. To my understanding the determinant should be a (albeit high order) polynom, too. And the paper, I ...
2
votes
1answer
152 views

Plot 3D boolean Array or matrix in Mathematica

I have been attempting several methods to plot a 3D diagram of a n by n boolean array in Mathematica but none of them produced satisfactory result. I want the $3D$ plot to have a cube when ...
0
votes
1answer
135 views

Simplify matrix into an upper triangular matrix

I have a tridiagonal matrix that I am trying to simplify into an upper triangular matrix using Mathematica, so I can use back substitution and solve my linear system. I have found the command ...
2
votes
1answer
91 views

Problem with Eigenvectors when given a matrix containing approximate numbers and symbols

I'm trying to diagonalize a certain 2 x 2 matrix, but Mathematica refuses to find the eigenvectors. In particular, when I input ...
10
votes
3answers
2k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
2
votes
2answers
265 views

Optimization problem with matrix positivity constraints

Is it possible for Mathematica to parametrically find a local minimum of a given function (say of some variable $x$ where $(a,b,c)$ serve as parameters) subject to the constraint that a given ...
2
votes
1answer
126 views

How to handle a sparse array of lists

I have data in the form of a sparse array of lists. For example: ...
3
votes
3answers
208 views

Finding a better way to define a matrix

I first defined a 171x171 matrix containing only zeros and then replaced 18 specific rows with nonzero entries. The other $153$ rows will be average of $2$ of the existing $18$ rows. Rows $2$ ...
5
votes
1answer
153 views

How to combine matrix with array without cycles?

I am new to Mathematica. And I'm sorry for my English. I have created a matrix ($6 \times 4$) and an array ($1 \times 4$). I want to get another matrix that will have the first element from the array ...
0
votes
0answers
86 views

Eigenvectors for a large symbolic matrix

I'm trying to compute the eigenvectors for a 42x42 symbolic matrix (with one variable) in Mathematica. I get the following error: Eigenvectors::eivec0: Unable to find all eigenvectors. >> and the ...
4
votes
3answers
239 views

Approximate minimum degree permutation algorithm in Mathematica

In MATLAB there is a nice implementation of the so called AMD (approximate minimum degree permutation) algorithm named amd (see Online MATLAB Documentation). There is an alternative algorithm called ...
14
votes
1answer
302 views

Making Monte Carlo simulation with ParallelTable

I would like to to MonteCarlo simulations of various regressions - basically, doing OLS under various conditions to test approaches. On my macpro 2x 2.8 GHz quad core Xeon, 32 Gb RAM DDR2 @ 667 Mhz, ...
1
vote
3answers
333 views

How to expand the size of the matrix automatically?

I have a matrix in 2x2 a ={{x, y}, {z, u}} I want to expand this matrix 3x3 b ={{x, y, y}, {z, u, x}, {z, x, u}} 4x4 ...
0
votes
0answers
457 views

Fastest way to create a NxNxNxN dimensional matrix

I have a function that outputs a complex number Func[x_,y_]:= blah blah; I have constructed a table of all possible values of this function. ...
1
vote
1answer
107 views

Matrix substitution

I'm newbie in Mathematica and would like to ask one simple question. Let's say I have matrix with some elements == -1 ...
0
votes
1answer
139 views

Specific entry of inverse of large matrix

Given a large (say 10x10) sparse Hermitian matrix with symbolic entries, I need four specific entries of the inverse matrix. It seems wasteful to me to compute 100 entries of which I only need a few ...
0
votes
1answer
83 views

Populating an array with outputs of a function [closed]

I have searched, but didn't find much help on my issue. I have an optical physics problem that I'm working on .. ...