Questions on the linear algebra functionality of Mathematica.

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2
votes
3answers
207 views

Selecting terms containing some expression

Imagine I have an expression like a*k + (a^2)*b*c + b*e and I would like to obtain the term containing, for example, some power of a. In that case I would ...
0
votes
1answer
614 views

Decoupling system of differential equations

Here I have one task and it is preparation for small exam. I solved it by hand for first case 1), but I need to check it in $Mathematica$ and to try to implement it for both cases 1) and 2) ...
6
votes
1answer
218 views

How to create a large sparse block matrix

I need to generate a very large sparse block matrix, with blocks consisting only of ones along the diagonal. I have tried several ways of doing this, but I seem to always run out of memory. The ...
9
votes
0answers
385 views

More efficient matrix-vector product

Dear mathematica users, In my present research I am faced with a real dense $n\times n$ matrix $A$ where $n \geq 3000$ (hopefully even more). The coefficients of this matrix are fixed, but I will ...
10
votes
2answers
299 views

Compiling LinearSolve[] or creating a compilable procedural version of it

Earlier today I had a discussion with a representative at Premier Support about the 2 questions I've asked here over the past couple of days: Seeking strategies to deploy a function securely ...
3
votes
3answers
288 views

Correct way to populate a DiagonalMatrix?

I would like to create a series of correlation matrices that starts with : sensMat[[1]] = DiagonalMatrix[ { 1,1,1,1,1 } ]) // MatrixForm and iterates in 0.1 ...
27
votes
2answers
2k views

How can I improve the speed of eigenvalue decompositions for large matrices?

I often need to compute the eigenvalues of large matrices, and I invariably resort to MATLAB for these, simply because it is much faster. I'd like to change that, so that I can work entirely inside my ...
3
votes
2answers
956 views

Linear equation with complex numbers

I have to solve an equation of the type $$a z+b \overline{z}=c$$ with $a,b,c\in\mathbb{C}$. My approach is to set $F(z)=a z+b \overline{z}-c$ transform $z$ to $x+i y$ and then get a real linear ...
1
vote
1answer
186 views

Functions that operate on symbolic matrices?

I'd like to write functions that operate on symbolic matrices, and do nothing when fed anything else. ...
9
votes
1answer
251 views

Verifying and deriving basic (block) matrix identities

How can I use the new symbolic matrix/tensor capabilities to verify matrix identities, such as (1) or (2) Even better, how can I ask Mathematica to derive expressions for X, Y, Z, and U like ...
6
votes
1answer
118 views

LinearSolveFunction unusable if stored to disk?

I encounter a problem when saving a LinearSolveFunction to disk, where the LinearSolveFunction is obtained with LinearSolve for ...
10
votes
2answers
673 views

Is there any way to obtain an approximate inverse for very large sparse matrices?

I have a very large sparse matrix and I need to obtain its approximate inverse and save it as an sparse matrix too. Any of my efforts as could be seen in what follows fail for large n ...
1
vote
0answers
170 views

Parallel linear algebra with arbitrary precision

Is it possible to do parallel linear algebra with arbitrary precision within Mathematica (in a simple manner, as is done for the machine precision)?
2
votes
2answers
381 views

Eigensystem, Eigenvalue doesn't output nonreal eigenvalues

Basically I have a matrix and when I used either Eigenvalue or Eigensystem, it doesn't output nonreal eigenvalues, instead it ...
9
votes
4answers
496 views

Dual-Grid Graph Paper With Mathematica?

Is there a slick way to generate the dual-grid graphs such as you can see on pages 7, 9, and 10 of this article, or this one? I've searched, but found nothing. Thanks in advance...
0
votes
1answer
157 views

Rearranging a biclustered matrix

I currently have a $77\times 38$ matrix, and I have used a clustering algorithm to cluster the row data and column data. The rows and columns of my matrix correspond to a list of country codes (not in ...
2
votes
3answers
214 views

Adding elements in the sublists

How can I add the elements in the sublists? For example, if I have the list which is m={{1,3},{2,3},{4,1}} then, the output that I want is ...
3
votes
2answers
249 views

Deleting a row or column of an adjacency matrix while maintaining the associated label

I am currently working with a weighted adjacency matrix for a directed graph, and it contains several 0 columns and rows. With the unaltered matrix, I am able to monitor the relations between vertices ...
5
votes
2answers
524 views

Can the CholeskyDecomposition function in Mathematica be made to work on non-symmetric matrices?

The CholeskyDecomposition[m] function in Mathematica requires a symmetric and positive definite matrix m. For instance, the ...
1
vote
1answer
587 views

Using singular value decomposition for graph clustering

I have a fairly large graph (50-60 vertices) with directed, weighted edges, and I am attempting to cluster the vertices. Prior to this, I have only worked with undirected graphs having symmetric ...
1
vote
1answer
528 views

Calculating an exact orthogonal modal matrix in Mathematica

I can calculate the modal matrix of a matrix A using the command JordanDecomposition[A][[1]], and a decimal approximation of the orthogonal (or normalised) modal ...
3
votes
2answers
539 views

Subspaces in Mathematica

I'm working on a research project and I need to learn how to use Mathematica to calculate subspaces. Specifically I plan to solve the following operations and I would greatly appreciate if you could ...
2
votes
2answers
802 views

Generating a vector of dummy variables

So I'm the situation of needing analytical solutions to a family of equations of the form Ax=b, where A is an nxn matrix. I've written a function that does what I want, but I'm currently using a bit ...
6
votes
2answers
1k views

Eigenvalue / Eigenvector Calculation

I'm currently trying to compute the three smallest eigenvectors for a 34 by 34 matrix. While I was expecting this to take some time, Mathematica has been running for the past 3 hours, which seems ...
5
votes
1answer
1k 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: ...
6
votes
3answers
695 views

Determine if solution to linear system exists

I'm trying to determine only if a solution to a linear system of equations exists. I have been using LinearSolve, which works fine, but it solves the system as ...
9
votes
3answers
377 views

Toggle visibility of elements in a plot

I have three simple graphs in one Plot. Now I am trying to make a button for each graph so you can hide or show it in the plot. Until now I was just able to make a checkbox with the Manipulate ...
2
votes
3answers
711 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 ...
13
votes
3answers
1k 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 ...
1
vote
1answer
543 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
462 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 ...
3
votes
4answers
154 views

Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
10
votes
3answers
913 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.
20
votes
3answers
547 views

Computing polynomial eigenvalues in Mathematica

MATLAB offers a function polyeig for computing polynomial eigenvalues, which appear, for instance in quadratic eigenvalue problems (see here for some applications) such as: \begin{equation} ...
8
votes
1answer
358 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 ...
13
votes
1answer
510 views

Is there a clean way to extract the subspaces invariant under a list of matrices?

Let's say I have some $n \times n$ square matrices $A_1, A_2, \ldots, A_m$ with exact numbers for entries, and I want to find the subspaces of $V = \mathbb{C}^n$ invariant under these matrices. Is ...
3
votes
0answers
171 views

LeastSquare Solution for the Continuous Time Lyapunov Equation

I have been working with a problem which involves solving the continuous time Lyapunov equation $$A R + R A^\top = G$$ for the symmetric positive definite matrix $R$. Here $A$ is real, invertible ...
7
votes
1answer
410 views

Very fast way to do a coordinate frame transform

I need a function that rotates and translates a huge amount of line segments. For example, I have a set of line segments in the form {{x0,y0,z0},{x1,y1,z1}} ...
0
votes
1answer
500 views

If I know the steady state vector of a stochastic matrix, can i recover the matrix? [closed]

By steady state vector I mean the eigenvector which has an eigenvalue of 1. So is there a way to at least iteratively approximate the entries of the stochastic matrix? Thanks.
5
votes
1answer
475 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 ...
3
votes
2answers
1k 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 ...
10
votes
2answers
1k views

Find Determinant/or Row Reduce parameter dependent matrix

I'm trying to find the determinant of a band diagonal matrix that has a parameter, $\kappa$, in some of the entries. Some entries are just numerical ones, others ($\kappa$ X number), while others are ...
12
votes
4answers
406 views

How do you decompose a polynomial matrix into its 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 ...
14
votes
3answers
776 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 ...
4
votes
1answer
531 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 ...
5
votes
1answer
374 views

Tridiagonal symmetric matrix eigenvalue using bisection

I know that Eigenvalues is already quite well implemented in Mathematica, nor am I foolishly trying to improve on it. In order to improve my programming skills, I ...
5
votes
3answers
767 views

Solution for equation system with piece-wise defined functions

As I could swear this worked just yesterday, I am probably just doing something stupid here and I am sorry to bother you :) I am trying to find the point where a curve crosses a line. In this case, ...
3
votes
2answers
1k 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 ...