Tagged Questions

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.

343 views

Possible Method for MatrixExp

Well, probably a hard question, but I think it's better to cry out loud :). I noticed that MatrixExp has a Method option when ...
61 views

MatrixExp[m, v] not always faster than MatrixExp[m].v

For non sparse matrix m, is MatrixExp[m, v] supposed to be faster than MatrixExp[m].v? ...
37 views

Make NSolve faster by keeping only one solution

Dear Mathematica users, NSolve usually returns all numerical solution it can find. When a variable is squared in some equation, ...
63 views

Large matrix: Finding eigenvalues and ordering it with respec to the highest coefficient of its eigenvectors

I have a 900x900 matrix to diagonalize. After diagonalizing it, I have a table of eigenvalues and eigenvectors. For convenience, I start with 3x3 matrix. ...
69 views

Improve speed of Nested Matrix exponential

I have a short Code example and I want to know whether it is possible to improve the speed. The L matrix in my code is a SparseMatrix, but for this question I just use something similiar. ...
58 views

Eigenvalues of large symmetric matrices

When I try to compute the eigenvalues of the adjacency matrix of a very large graph I get, what can be charitably described as, garbage. In particular, since the graph is four-regular, the eigenvalues ...
167 views

Create a 900x900 matrix and diagonalize it

I have to create a 900x900 matrix and then diagonalize it. It is something similar to the below matrix. The value of a,b,c,d....up to 900 values (which are the first column and row) are the number. ...
80 views

Gram-Schmidt Process

I've discovered the Orthogonalize command: Clear[x1, x2] x1 = {1, 1, 0}; x2 = {-2, 0, 1}; Orthogonalize[{x1, x2}, Method -> "GramSchmidt"] Which returns an ...
213 views

Solve a system of M equations without specifying M [on hold]

I am trying to write my game-theoretic model in Wolfram Language. There is only one remaining step and I am not sure if it is within reach of Wolfram Language (or Mathematica). I describe a simplified ...
37 views

Mathematica Not finding Eigenvectors? [duplicate]

I have the following matrix: mat = {{-60., 0., 2.1*10^-35 II + 2.1*10^-35 (-1. II + Istar), 2.1*10^-35 II + 2.1*10^-35 (-1. II - 4.7619*10^6/Istar)}, {-6.4*10^22 II - 6.4*10^22 (-1. II - ...
332 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] ...
56 views

Creating a Symbolic Singular Matrix

I am trying to differentiate an expression involving a matrix. When evaluating the input, Mathematica assumes the matrix is invertible, when it is not. How do I specify a symbolic singular matrix to ...
71 views

Generating plane equation from LinearSolve

I will ask a simple question and might have an issue on the site that explains better about it, but not found. I am formulating a code that defines me an equation that I can generate a plot. ...
27 views

System of Inequalities with symbolic parameters

I am trying to solve the following system of inequalities in Mathematica but the output is just the same system of inequalities. I need to get the expressions for ...
233 views

Generating a vector basis

I have several lists parameterizing a vector space, for instance {a[1],a[2],a[1]+2 a[2]-a[3]} For each list I want to generate a basis such as ...
173 views

GridLines for a coordinate system with a particular basis

Suppose that I use the vectors $(2,1)$ and $(-1,1)$ as a basis for $R^2$. ...
58 views

Why am I losing precision in computation of eigenvectors of sparse matrices?

I compute the eigenvectors and eigenvalues of the same matrix in its dense and sparse version. The eigenvalues are the same to great precision, but the eigenvectors are not: when I compute the ...
82 views

A question on JordanDecomposition in Mathematica

How can I have Mathematica show me also the inverse matrix of the similarity matrix of JordanDecomposition of a matrix? Obviously I need to use here the ...
106 views

Grabbing the independent columns of a matrix A

I found a nice way to generate a random $5\times 7$ matrix with rank 3. MatrixForm[A = RandomInteger[5, {5, 3}].RandomInteger[5, {3, 7}]] MatrixRank[A] Let me ...
407 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. ...
3k views

How do I keep the right ordering of eigenvalues using Eigensystem?

I'm having an issue with the Eigensystem command. I need to diagonalize a bunch of 3 by 3 complex valued matrices, but more importantly, I need to keep the exact ...
320 views

Bilinear Dot Function

In mathematics the matrix product is a bilinear operation $$\alpha A \cdot(\beta B + \gamma C) = \alpha\beta ( A \cdot B )+ \alpha \gamma (A\cdot C ),$$ where capital letters denote matrices and ...
143 views

Why FindMaximum doesn't work in my example

Consider the following function ...
34 views

Finding the magnitude a matrices [closed]

I need some help. I have a list of 3 x 3 matrices of real numbers.I want to find how close each of these matrices are to a {{0,0,0},{0,0,0},{0,0,0}} matrix. Any suggestions to a method algorithm or ...
120 views

The new introduced EulerMatrix problem

In the present version of Mathematica, there is a new command EulerMatrix[{α, β, γ}])// MatrixForm I read its document and I still don't understand it. For me, ...
335 views

Cross product between two lists of vectors

I'm trying to create a function that does the cross product between two lists of the same dimensions, element by element. Each entry of the list is a 3D vector. Something like this: ...
64 views

Counting flops to compare to operations

I know there is a Timing approach, but I am wondering if there is a Mathematica command that will count the number of flops (floating point operations). For example, if I do: ...
71 views

Aguilera-Perez Algorithm of $nD$ rotation matrix [closed]

I want to compute a general $nD$ rotation matrix which corresponds to a rotation by an angle $\theta$ around an $(n−2)$-dimensional subspace. I found the Aguilera-Perez algorithm in their paper: ...
57 views

Problem with Volume and Parallelepiped [closed]

This worked (copied from the documentation), and gave correct image with Graphics3D. R = Parallelepiped[{0, 0, 0}, {{1, 0, 0}, {1, 1, 0}, {0, 1, 1}}]; Volume[R] ...
106 views

Expanding a matrix in a set of matrices

Consider a vector $a=\{a1,a2,a3\}$. I computed $e^{i a\cdot \sigma}\qquad \sigma: {\rm Pauli\ matrices}$ and then applied the command ExpToTrig. Now I want to expand the above result in terms of ...
75 views

Gauss-Jordan program in Mathematica

Hi to everyone I made this program to solve a linear system by Gauss Jordan, this is my code to solve the system: ...
120 views

193 views

Eigenvectors of numerical matrix

I have a large numerical matrix whose eigenvalues are all distinct. In the documentation for Eigenvectors it says: For approximate numerical matrices m, the ...