Questions on the linear algebra functionality of Mathematica.

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2
votes
2answers
628 views

Generating a vector of dummy variables

So I'm the situation of needing analytical solutions to a family of equations of the form Ax=b, where A is an nxn matrix. I've written a function that does what I want, but I'm currently using a bit ...
5
votes
2answers
1k views

Eigenvalue / Eigenvector Calculation

I'm currently trying to compute the three smallest eigenvectors for a 34 by 34 matrix. While I was expecting this to take some time, Mathematica has been running for the past 3 hours, which seems ...
5
votes
1answer
946 views

Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong?

If I ask Mathematica to find the eigenvectors and eigenvalues of the matrix: ...
6
votes
3answers
599 views

Determine if solution to linear system exists

I'm trying to determine only if a solution to a linear system of equations exists. I have been using LinearSolve, which works fine, but it solves the system as ...
9
votes
3answers
339 views

Toggle visibility of elements in a plot

I have three simple graphs in one Plot. Now I am trying to make a button for each graph so you can hide or show it in the plot. Until now I was just able to make a checkbox with the Manipulate ...
2
votes
3answers
640 views

Finding eigenvalues of a $1500\times1500$ matrix

I need to find the eigenvalues of a $1500\times1500$ real symmetric matrix given by $A_{i,i+1}= A_{i+1,i}=-1$ and also $A_{1,N=1500}=-1$ (this is because of a periodic boundary condition used) and all ...
13
votes
3answers
926 views

Mathematica for linear algebra course?

I'm taking a linear algebra / matrix theory course and we are free to use any software we want, and will be "expected to use MATLAB or an equivalent" for homework. The professor and textbook (Applied ...
1
vote
1answer
518 views

Is Mathematica matrix multiplication with its inverse wrong? [duplicate]

Possible Duplicate: Why don't * and ^ work as I expected on matrices? When I enter this ...
1
vote
2answers
430 views

How to Solve or LinearSolve $A = I$ matrix equation?

I'd like to solve this equation for $A = B$ where $B = I$, which represents 3 systems of 3 linear equations, for $a, b, c, d, e, f$, without writing LinearSolve 3 ...
3
votes
4answers
148 views

Pack Solve results into a vector

I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace: ...
10
votes
3answers
854 views

Correcting a correlation matrix to be positive semidefinite

Does Mathematica have a way to "fix" a correlation matrix that is not positive semi-definite? I looked through the documentation and search the internet but could not find anything.
20
votes
3answers
515 views

Computing polynomial eigenvalues in Mathematica

MATLAB offers a function polyeig for computing polynomial eigenvalues, which appear, for instance in quadratic eigenvalue problems (see here for some applications) such as: \begin{equation} ...
8
votes
1answer
340 views

Efficiently Constructing Rank One Approximations for a Matrix using SVD

Suppose I have a $m\times n$ matrix $A$ (real for simplicity). Then SingularValueDecomposition[A] yields 3 matrices $U$, $\Sigma$ and $V$ such that $A = U\Sigma ...
13
votes
1answer
466 views

Is there a clean way to extract the subspaces invariant under a list of matrices?

Let's say I have some $n \times n$ square matrices $A_1, A_2, \ldots, A_m$ with exact numbers for entries, and I want to find the subspaces of $V = \mathbb{C}^n$ invariant under these matrices. Is ...
3
votes
0answers
166 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 ...
7
votes
1answer
380 views

Very fast way to do a coordinate frame transform

I need a function that rotates and translates a huge amount of line segments. For example, I have a set of line segments in the form {{x0,y0,z0},{x1,y1,z1}} ...
0
votes
1answer
892 views

Solve matrix equation A*X=X*B using LeastSquares

I want to solve matrix equation A*X=X*B using LeastSquares method, but it is suited for equation like A*X=B. All matrices are 3x3 ...
0
votes
1answer
442 views

If I know the steady state vector of a stochastic matrix, can i recover the matrix? [closed]

By steady state vector I mean the eigenvector which has an eigenvalue of 1. So is there a way to at least iteratively approximate the entries of the stochastic matrix? Thanks.
5
votes
1answer
434 views

Finding the characteristic polynomial of a matrix modulus n

Given a square matrix, is it possible to calculate its characteristic polynomial modulo n? Unfortunately, this function ...
3
votes
2answers
938 views

Matrix multiplication in Block Form symbolic calculation by Mathematica

I have a problem which requires taking product of two $10\times10$ matrices. I would like to do it by considering both matrices as $5\times5$ matrices such that each entry of both matrices is actually ...
10
votes
2answers
937 views

Find Determinant/or Row Reduce parameter dependent matrix

I'm trying to find the determinant of a band diagonal matrix that has a parameter, $\kappa$, in some of the entries. Some entries are just numerical ones, others ($\kappa$ X number), while others are ...
12
votes
4answers
396 views

How do you decompose a polynomial matrix into its matrix coefficients?

Let's say I have a matrix, $\mathbf{M}$, that is polynomially dependent on a single variable, such as M = {{15 + a^2, a + 5 a^2}, {a - 5 a^2, 2}} and I want to ...
14
votes
3answers
713 views

Constructing a symbolic Hermitian matrix

I need to construct a symbolic Hermitian matrix like m = { { n, a, b, b}, {Conjugate[a], n, b, b}, ... } but I am not able to set ...
4
votes
1answer
495 views

Computing Slater determinants

I need to compute Slater determinants. I'm wondering if I would benefit from assigning each of my functions to a variable prior to computation. I'm working with Slater determinants, but my question ...
5
votes
1answer
359 views

Tridiagonal symmetric matrix eigenvalue using bisection

I know that Eigenvalues is already quite well implemented in Mathematica, nor am I foolishly trying to improve on it. In order to improve my programming skills, I ...
5
votes
3answers
723 views

Solution for equation system with piece-wise defined functions

As I could swear this worked just yesterday, I am probably just doing something stupid here and I am sorry to bother you :) I am trying to find the point where a curve crosses a line. In this case, ...
3
votes
2answers
986 views

How to substitute numeric values in a symbolic Jacobian matrix?

I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
11
votes
1answer
436 views

Space-efficient null space of sparse array

I have a roughly 100,000 × 3,000 matrix (as a SparseArray) that I'd like to find the kernel (null space) of. It has about 500,000 nonzero entries, all -1 or 1. ...
6
votes
0answers
218 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. ...
9
votes
1answer
267 views

Memory Leak in RowReduce?

Recently I tried to do what I thought was a fairly small (relative to the 6 GB of RAM that I have on my machine) row reduction calculation on a matrix representing an undetermined linear system and ...
10
votes
2answers
445 views
5
votes
1answer
854 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 ...
11
votes
1answer
530 views

What is the fastest way to find an integer-valued row echelon form for a matrix with integer entries?

Let me begin by saying that this is my first post on StackExchange. I apologize in advance if I unwittingly break any of its unwritten rules of etiquette. Recently, I've been trying to understand an ...
6
votes
0answers
273 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 ...
17
votes
3answers
2k views

How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, ...
0
votes
1answer
394 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 ...
3
votes
2answers
473 views

Solving a linear equation in Mathematica

This should be easy but I can't seem to find the right way to do it. I have an equation of the form $a x + b x + c y + a z + d z = 0$, and I'd like to solve for relations between the parameters ...
2
votes
3answers
796 views

Orthonormalization of non-hermitian matrix eigenvectors

When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
7
votes
2answers
582 views

Entering block matrices for an arbitrary matrix size

Background: How to enter matrices in block matrix format? and the following: I want to create $$ f(A,t) = \left [ \begin{matrix} A & t \\ 0 & 1 \end{matrix} \right ] $$ where $A$ ...
4
votes
3answers
862 views

Trying to simplify Root expressions from the output of Eigenvalues

I am trying to calculate eigenvalues of a sparse matrix with only two distinct non-zero elements, here Alpha and Beta, which are both negative reals. Mathematica returns some complex expressions with ...
1
vote
0answers
256 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 ...
4
votes
2answers
420 views

ordering of functional eigenvalues

Is there any order to the symbolic eigenvalues of a matrix returned by the command Eigenvalues[...]? While numerical eigenvalues are listed in descending order ...
4
votes
1answer
276 views

Obtaining a thin/compact SVD

I'm using SingularValueDecomposition for a least-squares regression, the instruction that works fine for what I need is ...
10
votes
3answers
849 views

Can Eigenvalues[] and Eigenvectors[] be assumed to return the same ordering?

If I do back to back calls of Eigenvalues[] and Eigenvectors[] can these be assumed to order the values and vectors the same, or ...
3
votes
1answer
794 views

Obtaining the square-root of a general positive definite matrix

I have a matrix which I know to be positive definite. The entries of the matrix might be complicated but they are all real. To find an expression for the square root of this matrix (i.e., ...
4
votes
1answer
279 views

How to fix errors in Gram-Schmidt process when using random vectors?

I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
11
votes
1answer
301 views

Why is MainEvaluate being used when LinearSolve can be compiled?

According to this question LinearSolve can be Compiled. However, CompilePrint shows a MainEvaluate but no-warning is generated. It appears that LinearSolve is not ...
4
votes
0answers
213 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 ...
16
votes
2answers
2k views

How to enter matrices in block matrix format?

Example: I have a matrix $R = \left( \begin{array}{cc} A & \mathbf{t} \\ 0 & 1 \end{array} \right) $ where $A$ is 3-by-3 and $\mathbf{t}$ is 3 by 1. Or in Mathematica ...