Questions on the linear algebra functionality of Mathematica.

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0
votes
1answer
248 views

Why is EigenValues returning Root expressions?

This is the code I have: ...
0
votes
1answer
88 views

Why does Eigenvalues[matrix I defined] not work? [duplicate]

This is the code I have in my mathematica notebook. I want to find the eigenvalues of the matrix I created called Hmatrix as defined below. However when I type Eigenvalues[Hmatrix] I get the Hmatrix ...
3
votes
1answer
257 views

How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
0
votes
1answer
154 views

Interpolating a Bivariate Polynomial over a Finite Field

Let $F=GF(p)$ be a finite field, $p$ prime and write $F^\times=\{x_1,\ldots,x_n\}$. I'm trying to implement an earlier version of Sudan's list-decoding algorithm for Reed Solomon Codes ...
5
votes
2answers
2k views

Solving a tridiagonal system of linear equations using the Thomas algorithm

I'm trying to write a function that can solve a tridiagonal system of linear equations using the Thomas algorithm. It basically solves the following equation. (Details can be found at the Wiki page ...
5
votes
1answer
474 views

Octonions in Mathematica

Is there a package or Notebook for Mathematica that can enable me to do some numerical calculations with octonions? Maybe a way to plug-in the octonion multiplication table?
10
votes
1answer
883 views

Eigenvalues and Determinant of a large matrix

Can anybody kindly explain to me what is going wrong regarding a simple problem I have? I can find the eigenvalues of a large matrix using Eigenvalues[], but when I ...
1
vote
1answer
70 views

Confirming the existence of a function related to a matrix

Is it possible to get an answer to the following question in Mathematica? Let $M$ be a $n$ by $n$ matrix, is there a function $m:\mathbb{N}\times \mathbb{N}\rightarrow \mathbb{Z}$ such that ...
6
votes
1answer
460 views

TensorContract of inverse matrix

Matrix inverse in mathematica If $A$ is an invertible $n \times n$ matrix, then $A\cdot A^{-1} = I$. To get this statement in Mathematica, you need the assumption ...
9
votes
2answers
277 views

Speed up 4D matrix/array generation

I have to fill a 4D array, whose entries are $\mathrm{sinc}\left[j(a-b)^2+j(c-d)^2-\phi\right]$ for a fixed value of $\phi$ (normally -15) and a fixed value of $j$ (normally about 0.00005). The way ...
7
votes
2answers
1k views

Badly conditioned matrix (General::luc)

With some matrices I am receiving the following message ...
2
votes
1answer
187 views

Can I reduce a matrix inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$?

I'm new to Mathematica. When I do linear algebra, I wonder if I can have an inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$, where $\mathbf x$ is a column vector ...
1
vote
0answers
118 views

How to express this output in the form $X=A.x$?

This problem arose in my stereo vision project. I have two matrices: $$ A = \left( \begin{array}{ccc} \text{x1}*\text{p131}-\text{p111} & \text{x1}*\text{p132}-\text{p112} & ...
0
votes
1answer
542 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) ...
2
votes
3answers
155 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 ...
6
votes
1answer
188 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
344 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
282 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
277 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 ...
3
votes
1answer
216 views

Evaluating a function on permutations of its arguments

Say I have a function "temp" of $n+1$ variables, $y,z1,z2,z3,...,zn$. I want to test if my function has certain symmetries like swapping $y$ with square of any $z$, swapping any two of the zs, ...
2
votes
1answer
321 views

RowReduce: Solving for the resource vector (a, b, c) in Augmented Matrix

Here are two examples: RowReduce[{{3, 1, a}, {2, 1, b}}] evaluates to {{1, 0, a - b}, {0, 1, -2 a + 3 b}} but ...
3
votes
2answers
848 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
179 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
229 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 ...
1
vote
0answers
249 views

Matrix algebra vs. PrincipalComponents and Varimax/Oblimin

Using matrix algebra I can calculate loadings and scores from the covariance matrix (data matrix is column centered): ...
1
vote
0answers
165 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
1answer
414 views
2
votes
2answers
377 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
475 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
155 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
196 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
222 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 ...
4
votes
2answers
460 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
480 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 ...
6
votes
1answer
117 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 ...
3
votes
3answers
265 views

Proving a recurrence in Mathematica

I have $$j_n=\int_0^1 x^{2n} \sin(\pi x)dx.$$ How do I show that $$j_{n+1}= \frac{1}{\pi^2}(\pi- (2n+1)(2n+2)j_n)\, ?$$ I keep getting a recurring integration by parts and I can't simplify it. ...
1
vote
1answer
492 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 ...
4
votes
2answers
373 views

How to solve an eigensystem faster?

I have a module that I need to call 1-10 million times in my program. Currently, it is taking several hours to run so I am hoping that I can cut down some runtime with your help. ...
3
votes
2answers
492 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
629 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 ...
5
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 ...
2
votes
1answer
495 views

Linear Solve with Modular Arithmetic

I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
5
votes
1answer
946 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
599 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
339 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 ...
10
votes
2answers
217 views
2
votes
3answers
640 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 ...
1
vote
1answer
518 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
430 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 ...
13
votes
3answers
926 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 ...