Questions on the linear algebra functionality of Mathematica.

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34 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 ...
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26 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
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0answers
42 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 ...
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0answers
64 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 ...
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0answers
31 views

Symbolic computation under certain assumptions [duplicate]

Assume that I have a matrix $M$ and I'm doing some operations on it. Is there a way to specify that two variables satisfy an equation say $x=y^2$ and then let Mathematica compute under that ...
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0answers
64 views

Steps in row reduction? [closed]

I have a fully symbolic matrix that I'm row reducing. Looking at the end result, I see that Mathematica must have divided out some common factors for each row. However, I need to analyze those ...
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0answers
81 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.
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0answers
113 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 ...
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0answers
75 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 ...
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96 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 ...
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105 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 ...
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76 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: ...
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1answer
235 views

Gram Schmidt inner and outer products

I know the Gram-Schmidt orthogonalization generates an orthonormal basis from an arbitrary basis. I need help with: Write a program that inputs a list $\{b_1,\dotsc,b_n\}$ of linearly independent ...
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144 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 ...
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348 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 ...
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0answers
125 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} & ...
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1answer
201 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. ...
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0answers
185 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)?
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262 views

Matrix multiplication involving MatrixForm [duplicate]

Possible Duplicate: Why does MatrixForm affect calculations? I am doing a matrix multiplication, but not getting the desired output. I am doing the matrix multiplication of $A^{-1}B$ from ...
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2answers
300 views

Difference In Eigenvectors

When running my program in both Mathematica and MathCad, I end up with the same eigenvalues, but different eigenvectors. The ones in MathCad are normalized, which the documentation for Mathematica ...
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1answer
133 views

Differences between 'Solve' and 'LinearSolve' [closed]

Using the function 'Solve' I can do the following: Solve[a x + y == 7 && b x - y == 1, {x, y}] I get the following output: I want to get the same output using 'LinearSolve' instead. How ...
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2answers
164 views

Eigenvector Anomaly

I'm trying to compute the eigenvectors for: $$ M = \left( \begin{array}{ccc} 1 & 4 \\ 4 & 100 \end{array} \right) $$ Both myself and Mathematica report the eigenvalues as: $$ \lambda_1 = ...
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1answer
501 views

How to simulate the response of a linear parametric varying system in Mathematica?

Consider the following system \begin{align} \dot{x}(t)&=\sum_{i=1}^{2}\rho_{i}(x(t))\left[A_{i}x(t)+B_{i}u(t)\right]\\ y(t)&=Cx(t) \end{align} with: ...
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1answer
373 views

Why is EigenValues returning Root expressions?

This is the code I have: ...
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1answer
135 views

eigenvector bug also for matrix with numeric value [closed]

I just realize that probably there is a bug also in calculating the eigenvector of a matrix with numeric values (see here for bug in eigenvector calculation with symbolic value). In particular in my ...
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1answer
238 views

Projection of a set of 4D points to the 3D space

Consider the following set of points in the 4D space: ...
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1answer
45 views

Why `FindMaximum` doesn't work in my example

Consider the following function ...
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1answer
122 views

How smart is Solve? Figuring out what tricks I should try

I'm trying to solve a large system (~10000) of linear equations using Solve, but the process keeps failing. As-is, I don't know whether it's failing because it's using too much memory or too much time ...
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1answer
212 views

Performing matrix multiplications with a list

I have a question in regards to PseudoInverse. I have $A$, an $n\times 2$ matrix, and when I want to compute $(A^T A)^{-1}A$, by using ...
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1answer
177 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 ...
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1answer
864 views

Best way to compute row eigenvectors

Without qualification, the term eigenvectors (of a matrix) refers to the column eigenvectors (of a matrix) and can be directly computed with Eigenvectors[]. To get ...
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2answers
100 views

How to extend “List-of-numbers-with-number” arithmetic to “List-of-X-with-X” arithmetic? [duplicate]

I'll start with a couple of examples (since this is all one can get from the documentation anyway). First, adding lists of numbers equal length is done term-by-term. E.g. ...
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2answers
63 views

NSolve gives {{ x -> #}}, How do I make x = #; I need to use the x value again later

I want to use: demand = {1.92, 2.07, 2.37, 2.72, 2.87}*10^6; NSolve[SetV == demand[[1]]/(Cpf (1 - χ)), χ] I want to make a vector of solutions ...
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1answer
64 views

Submatrix with linearly independent columns

What I want is the submatrix where all the linearly dependent rows have been eliminated. I tried implementing this solution, but it doesn't work in the following example: ...
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1answer
57 views

How to tell Eigensystem the type of the elements comprising a matrix I would like to diagonalize

How can I tell Eigensystem that a matrix $M$, which I would like to diagonalize, is a numerical matrix of complex numbers? My idea is that this information could ...
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2answers
52 views

Modifying elements of a matrix after construction [closed]

Suppose I have constructed a matrix with all elements as a constant (say 1): N=4; A=ConstantArray[1, {N, N}]; Now I want to make A(2,3)=23 and A(4,3)=43. Can I ...
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1answer
63 views

Any command for group products?

Is there any Mathematica command or well known technique to take the direct product between two symmetric/permutation groups?
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1answer
114 views

How to power-series expand determinants?

Say $g$ is a matrix which is given as, $g = g_0 + xg_2 + x^2 g_4 .. +x^{d/2 -1}g_{d-2}+ x^{d/2}(g_d + h_d(log (x)))$ where $d$ is an even number and each $g_i$ is a matrix (same dimension as $g$) and ...
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1answer
244 views

How to create a 2D array (matrix) [closed]

I am pretty new to Mathematica. I need to create 2d array dynamicly. I got some code in C++(Qt) and it looks like this: ...
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1answer
211 views

Simplify matrix into an upper triangular matrix

I have a tridiagonal matrix that I am trying to simplify into an upper triangular matrix using Mathematica, so I can use back substitution and solve my linear system. I have found the command ...
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1answer
141 views

Why Eigenvalues thinks matrices are non-numerical

I use Mathematica version 9.0.1. ...
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1answer
93 views

LinearSolve symbolic equations

I am trying to use mathematica to solve the following system of equation, but I can not for the life of me get it to work. I have the following: ...
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1answer
90 views

How to find coordinates of an abstract vector relative to a basis

Let's say I have a degree 3 homogeneous polynomial over variables $x0, x1, x2.$ There are then 10 distinct monic monomials, forming a basis of the vector space of polynomials of degree 3. If I have ...
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1answer
183 views

Is it in general faster to get the eigenvectors and eigenvalues of a dense array rather than a sparse array?

I always thought that things in general go faster when working with sparse array but, I got this: Eigenvalues::arhm: Because finding 144 out of the 144 ...
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1answer
728 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) ...
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1answer
522 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 ...
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1answer
53 views

How to put constraints on NDSolve[] solution

Assumed the following example of double pendulum by Thison (Answered by Jens): Animation of double pendulum Imagine that in the given animation(i.e. http://i.stack.imgur.com/p4TgL.gif ), the second ...
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1answer
64 views

How large can be the dimension of a complex matrix which Mathematica can handle to find its eigenalues?

I have been working with 12 cross 12 complex matrix in Mathematica , I need to work with bigger size matrix of the dimension of the order of hundreds , I was wondering if Mathematica can handle ...
0
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1answer
34 views

I need help simplifying this equation [closed]

1 = D / R Now I want to add a value to each side. U. Is it like this? 1 + U = D / R + U Then I need it simplified. Thanks
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1answer
211 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 ...