Questions about Mathematica functionality related to manipulating vector spaces and linear mappings between such spaces. This includes determination of matrix properties, matrix transformations, decompositions, and factoring.

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15
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0answers
201 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 array with symbolic ...
10
votes
0answers
509 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 ...
6
votes
0answers
64 views

Choosing appropriate WorkingPrecision when solving numerical system of equations

Consider a linear system of equations, which is conveniently written as A.x=y. The matrix A has dimensions ...
6
votes
0answers
181 views

Calculating the rank of a huge sparse array

By virtue of the suggestion in my previous question, I constructed the sparse matrix whose size is $518400 \times 86400$, mostly filled with $0$ and $\pm 1$. Now I want to calculate its rank. Since ...
6
votes
0answers
311 views

How to produce the ILU0 or ILUT as stand-alone procedures on sparse matrices?

Mathematica uses the ILU0 procedures automatically to precondition large sparse linear systems; e.g. ...
6
votes
0answers
318 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 ...
6
votes
0answers
279 views

NullSpace[_, Method->“OneStepRowReduction”] is sometimes wrong; how can I work out when this happens?

Edit 2015: Has this been fixed yet? (This is on MMA 7.0.1.0 on OS X) I've just found a large matrix m for which NullSpace[m] ...
5
votes
0answers
41 views

Mathematica package for explicit matrix representations of group generators?

While there are several packages that are capable of working with weights and roots (for example LieArt), I couldn't find any package that spits out explicit matrices for the generators, for example ...
5
votes
0answers
1k views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
4
votes
0answers
202 views

Discriminant of Characteristic Polynomial

I'm doing a calculation which finds the characteristic polynomial of a matrix with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 ...
3
votes
0answers
85 views

LinearSolve and Krylov Method options

I need to solve a large, sparse, linear system. At some point Method -> "Multifrontal" fails and a bit later also "Pardiso" ...
3
votes
0answers
270 views

Fast principal component analysis

I'd like to speed up a principal value value analysis. The data contains a large set of vectors with a large dimension. Both are in the range of 1000. I want to obtain the loadings matrix for further ...
3
votes
0answers
289 views

How to compute the Lovász number for the given graph in Mathematica?

Here is a graph whose adjacency matrix is ...
3
votes
0answers
202 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 ...
2
votes
0answers
45 views

Explicitly find a guaranteed factorization of large expression?

Consider the large expression LE defined in this file (involving only linearly independent functions), or in this file (linear interdependence present but slightly ...
2
votes
0answers
74 views

Suggestions for solving a large linear system

I have a system of $\approx 200,000$ linear equations in $\approx 40,000$ variables (with rational coefficients) and I would like to determine the dimension of the solution space, which I know to be ...
2
votes
0answers
57 views

Derivative of vector dot product with respect to a vector

I have the expression: Transpose[gvecI, {2, 1}].x (m[1] + m[2]) gvecI and x are [3x1] ...
2
votes
0answers
50 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
2
votes
0answers
41 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
2
votes
0answers
62 views

MatrixRank of a large but sparse matrix

I want to find the rank of a very sparse, quite rectangular matrix mat, but I'm running out of RAM (I have 16 GB) if I try to use ...
2
votes
0answers
75 views

Simplify large fractions

Hi i'm quite new with Mathematica and i'm experiencing some problems with Simplify and FullSimplify. I'm dealing with a sistem ...
2
votes
0answers
22 views

What is the most efficient method to find a single eigenvector with eigenvalue that is numerically 0?

I need to find an eigenvector of a (numerically calculated) square matrix M corresponding to the eigenvalue 0. The methods I know are ...
2
votes
0answers
200 views

Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)

I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
1
vote
0answers
31 views

Linear Programming Using Dual Simplex method

I want to solve an optimization problem using the Dual Simplex Method. Although Mathematica gives the result directly when I use the command Minimize but I want to ...
1
vote
0answers
47 views

How to remove parts of an expression

I have an expression where terms Transpose[R].R appear. R is a matrix with the property Transpose[R].R=IdentityMatrix[3]. How ...
1
vote
0answers
35 views

Diagonal times dense matrix, high precision

I have a fixed dense matrix M of high precision numbers, say 40 by 40 and precision 40. Then I have a variable vector v of the ...
1
vote
0answers
48 views
1
vote
0answers
129 views

Find the smallest eigenvalue (not absolute value ) for a generalized eigenvalue problem

Related post Find the eigenvector associated with the smallest eigenvalue, not smallest in magnitude I tried to find the smallest eigenvalue for a generalized eigenvalue problem A c= \lambda B c ...
1
vote
0answers
47 views

Confusing NullSpace Method behaviour

The background of this question is that I'm trying to get the bottom of when the output of NullSpace outputs a list of pairwise orthogonal vectors. On my route to ...
1
vote
0answers
35 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
1
vote
0answers
78 views

Symbolic Nullspace computation in parallel

I am trying to determine the nullspace of a large symbolic matrix. The single core evolution seems to take too long. I tried Parallelize[] on the commands ...
1
vote
0answers
92 views

Request for clarification of Eigensystem::eivn message

What causes the problem of "two eigenvectors associated to one single multiplicity eigenvalue" that I am experiencing? After several transformations to simplify an unwieldy matrix, I end up with the ...
1
vote
0answers
117 views

The Jacobi-Davidson method

Does any implementation of the Jacobi-Davidson method for Mathematica exist? A highly parallelized version for sparse matrices would be of special interest.
1
vote
0answers
158 views

Diagonalization in parallel

I would like to diagonalize one unitary non-sparse matrix of size 12870 with complex number entries (not symbols, this is really a numerical problem). Is is possible to make eigensystem run in ...
1
vote
0answers
84 views

Find eigenvalues without filling the matrix

Is it possible to find eigenvalues of a matrix without filling it? The matrix elements are given by a known function f[p1,p2]. This is relevant for a matrix too ...
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 ...
1
vote
0answers
113 views

What is the fastest way to obtain the eigenvalues of a Wishart matrix?

I would like a fast method of creating a sample of random numbers which corresponds to the eigenvalues of a Wishart matrix: For M>N the eigenvalues \lambda_i are given by the jpd Where $K_N$ is ...
1
vote
0answers
152 views

Memory issue when using LinearSolve

When I use LinearSolve to solve a large system of linear equations where the left hand side is a matrix and the right hand side is a vector, the process takes a ...
1
vote
0answers
133 views

(Symbolic) LinearSolve is slower/different after upgrading to Mathematica 9

Yesterday I upgraded from mathematica 8.0.4.0 to 9.0.1.0. Trying to run the same notebook I used many times before, it takes ages to evaluate a symbolic (linearsolve) expression which before was ...
1
vote
0answers
81 views

How does TensorReduce use assumptions?

I would like to use TensorReduce by assuming that certain patterns of functions are tensors. From documentation of TensorReduce: ...
1
vote
0answers
207 views

RowReduce : Record of all the row operations for RREF

I read "for what right-hand sides $b=(a,b,c)$ does $Ax=b$ have a solution", but that question pertains to solving for the unknown vector. I'd like a record of all of the row operations required to put ...
1
vote
0answers
182 views

Conditional solution for system of linear equations

I have a linear equation system Q.m = t, with m unkown and where Q has dimensions ...
1
vote
0answers
448 views

Nontrivial solutions of equation

Here, I have one problem in finding nontrivial solutions of a system of equations. I want to choose one variable, for example X1 and to get solutions of X2(X1) and X3(X1). It is not difficult when I ...
1
vote
0answers
131 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} & ...
1
vote
0answers
198 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)?
0
votes
0answers
48 views

Compilable function with the functionality of SingularValueList

I'm doing something that involves finding the singular values of a lot of matrices. Basically I need to find singular values of $n$ matrices of dimension $n\times n$, where $n$ is as large as ...
0
votes
0answers
54 views

Is Eigensystem::eivin message a bug?

I noticed that in the question Request for clarification of Eigensystem::eivn message the error message Eigensystem::eivn: Incorrect number 2 of eigenvectors for eigenvalue ...
0
votes
0answers
56 views

Normalized, symbolic Eigenvectors without abs(), sign() etc

I'm trying to compute the normalized eigenvectors of a matrix M = {{0, 0, 0, 0}, {0, 0, M5, 0}, {0, M5, 0, M4}, {0, 0, M4, 0}} If I try Normalize ...
0
votes
0answers
47 views

CharacteristicPolynomial returns 0

I have the following matrix. ...
0
votes
0answers
46 views

Can LinearSolve use Parallelize and WorkingPrecision in computation

I am looking for a two things while calculating the large array matrix equation: 1) To increase the precision in simple LinearSolve[] function 2) To find a way to parallelize the computation on all ...