Questions on the linear algebra functionality of Mathematica.

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0
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1answer
625 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) ...
0
votes
1answer
452 views

On the parallelization of matrix multiplications in Mathematica 8

I have installed Mathematica 8, but I think the commands for parallelizations do not work! Even when I try to test the example in the Help of Mathematica, I face with ParallelDo::nopar: No ...
0
votes
1answer
192 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 ...
0
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1answer
62 views

Issues FindRootPlot command

I've had some fun playing around with FindRootPlot for a simple system of equations: ...
0
votes
2answers
435 views

Classification of a linear system of equations with a parameter

I need to get every possible value of k that returns infinite number of solutions or no solution to this system: ...
0
votes
1answer
165 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 ...
0
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0answers
20 views

What conclusions we can draw from $|A|$=0? if $A$ is a positive-semidefinite matrix [closed]

What conclusions we can draw from $|A|$=0? (the determinant is 0) $A$ is a positive-semidefinite matrix. Many thanks
0
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0answers
35 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
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0answers
66 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
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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
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0answers
46 views

Addition of sparse array objects [duplicate]

I have been having some trouble with the addition of large (but very sparse) matrices using SparseArray. Here is the simplest example to illustrate the issue. First, I will define diagonal matrices ...
0
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0answers
101 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
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0answers
185 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
112 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
97 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
422 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
0
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0answers
121 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?
0
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1answer
89 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 ...
-2
votes
1answer
52 views

$SU(4)$ Structure constants in mathematica

How can I write a mathematica function which will output arbitrary structure constants of SU(4)?
-4
votes
1answer
296 views

Solving Det[matrix] == 0 with an 8 x 8 matrix [closed]

I want to solve the equation Det[matrix] == 0 which came from the consistency of solutions of a set of 8 equations. This matrix has two constants λ and μ and two variables $P$ and $q$. I want to get ...