Questions on the linear algebra functionality of Mathematica.

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7
votes
1answer
218 views

Is it possible to implement symbolic sub matrices?

The accepted answer in the following link: http://stackoverflow.com/questions/5708208/symbolic-matrices-in-mathematica-with-unknown-dimensions provides a functionality to create symbolic matrices ...
2
votes
1answer
95 views

Proving positive definiteness or semi-definiteness of a matrix

I have the following 4x4 real symmetric matrix: $K=\begin{bmatrix}3-3w & -\frac{4}{3}+a+2w & \frac{5}{12}+b-\frac{w}{2} & 0\\ -\frac{4}{3}+a+2w & -1-6a-3x & ...
2
votes
1answer
86 views

Maximizing the number of zero entries in a matrix

I have a matrix with a bunch of parameters in its entries, they all come in different combinations in different places of the matrix. I can post the matrix itself if requested, but I think what I mean ...
8
votes
0answers
470 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
168 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
270 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
304 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 ...
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 ...
5
votes
0answers
248 views

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

(This is on MMA 7.0.1.0 on OS X) I've just found a large matrix m for which NullSpace[m] and ...
4
votes
0answers
181 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
75 views

Is there a way to do a symbolic PLUR decomposition of a matrix?

I am looking for a way to achieve the PLUR decomposition of a maitrx, as given in this paper here. The equivalent syntax in Maple is: ...
3
votes
0answers
155 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
272 views

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

Here is a graph whose adjacency matrix is ...
3
votes
0answers
196 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
48 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
177 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
65 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
36 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
26 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
1
vote
0answers
56 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
70 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
87 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
121 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
77 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
102 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
111 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
77 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
155 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
390 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
128 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
188 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
12 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 ...
0
votes
0answers
47 views

Calculating the rank of an abstract matrix

I'm trying to compute the rank of a 4x4 matrix with 4 parameters and 2 variables. I tried to calculate its rank under some assumptions on those conditions and I kept getting rank 4. So I did an ...
0
votes
0answers
32 views

Failure to evaluate functions of derivatives of Theta functions

I define a variant of the EllipticTheta function (multiplied by a constant factor) : ...
0
votes
0answers
79 views

Symbolic Tensor Algebra

I need to perform basic tensor algebra in order to double check some very complicated simplification. It's nothing fancy, it just has so many factors by the end that it's hard to tell if an error has ...
0
votes
0answers
49 views

Mathematica Numeric Output

I'm using Mathematica to compute barycentric coordinates, and the output for my points is not being computed, but rather it just shows it in the form that I inputted as. For example, I have: ...
0
votes
0answers
66 views

How to solve equations over polynomial rings

sorry if my question is very basic but I don't know what to even search to look it up and the only "obvious" places I thought of had nothing. Some background, for whatever context it might provide. ...
0
votes
0answers
153 views

Is there a way to solve the linear equation, Ax=b, in which A is a “non-constant” sparse matrix that depends on x?

I want to solve the Linear Equation, $Ax=b$ in Mathematica using Kylov subspace solver method preferably BICGSTAB(http://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method). Suppose ...
0
votes
0answers
136 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 ...
0
votes
0answers
219 views

Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
0
votes
0answers
175 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 ...
0
votes
0answers
125 views

Getting increased accuracy for roots of determinant

I have a matrix $a(\kappa)$ from which I am trying to determine $\kappa$ by using the equation $det(a(\kappa)) = 0$. The matrices I deal with are on the order of 100 X 100 to 500 X 500. Originally I ...
0
votes
0answers
180 views

how to solve a linear system (Ax=b) using domain decomposition?

The Domain decomposition is a natural technique for reducing the computational cost for solving large-scale linear systems, somebody know how to do it using mathematica?