Tagged Questions

Questions on the linear algebra functionality of Mathematica.

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1
vote
2answers
252 views

Finding maximal sublist of linearly independent vectors

Given a list of vectors v = {v1, ..., vn}, which is the fastest way to find a maximal sublist of linearly independent vectors? I could add the vectors one by one to ...
2
votes
1answer
640 views

How to simplify symbolic matrix multiplication results?

I've defined three symbolic abstract matrices X, M and S as shown below. ...
0
votes
2answers
479 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: ...
6
votes
1answer
633 views

Fastest way to do vector / matrix multiplication with constant matrix

Suppose we have a fixed n x n matrix, call it $B$. What is fastest way to evaluate $v^t B\;v$ over many different vectors $v$? Since $B$ is a constant matrix, does this allow the number of operations ...
3
votes
0answers
232 views

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

Here is a graph whose adjacency matrix is ...
7
votes
5answers
189 views

Selecting terms from a matrix

There are similar questions to this on the forum but none fit the purpose here: I would like to extract certain elements of a matrix depending on whether a factor is present or not, and create ...
0
votes
2answers
99 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. ...
5
votes
2answers
290 views

Faster Eigenvalues with lower precision goal

I compute all eigenvalues of a large matrix, and I decide that the speed is more important than the precision. Then the question is, can I speed up Eigenvalues[] by ...
5
votes
1answer
1k views

Solving a system of linear equations modulo n

I have a system of linear equations $$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$ What should I input (I'm using ...
3
votes
1answer
307 views

How can I get Mathematica to recognize equality of symbolic matrix expressions?

I have two matrix expressions: X.Transpose[T].Transpose[X] and X.T.Transpose[X] I want Mathematica to recognize that ...
2
votes
1answer
78 views

How can we use RowReduce with a modulous AND variables?

We can use RowReduce with a field. For example, we state RowReduce[{{1,3,5},{0,1,2}},Modulous->23] ...which then returns: ...
3
votes
2answers
476 views
10
votes
4answers
1k views

Axis/Angle from rotation matrix

With r=RotationMatrix[a,{x,y,z}] I can compute a 3D rotation matrix from axis/angle representation. Given a 3D rotation matrix ...
4
votes
1answer
238 views

Sporadic bug in Mathematica 7.01.0 MatrixPower and/or Eigensystem functions on floating-point symmetric matrices with repeated eigenvalues

Note: From the comments submitted below by other StackExchange users it appears that this apparent bug was fixed sometime after version 7.0.1. I asked a vague variant of this question a few days ago, ...
2
votes
1answer
210 views

How to obtain a Symplectic 4×4 matrix?

I have a problem in obtaining a $2n \times 2n$ Symplectic matrix $T$, with $n=2$. I couldn't find a direct command in Mathematica to achieve this. Conditions: ...
6
votes
1answer
410 views

Eigenvector corresponding to a specific eigenvalue already found earlier

just a quick question that is very simple but somewhat hard to explain. I am using 4 specific eigenvalues of a large 80x80 k-dependant matrix. I found the 4 eigenvalues of interest for various k and ...
-4
votes
1answer
318 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 ...
5
votes
0answers
918 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 ...
1
vote
1answer
95 views

sequence of matrix multiplications

My linear algebra book has questions that are are marked to use math software. There's probably some $50 guide on how to do everything but usually documentation has gotten me through. I've been kind ...
1
vote
1answer
108 views

Using Dot Product with InterpolatingFunctions

I am using NDSolve on a vector function $\mathbf y'(x)=f[\mathbf y(x)]$ with initial condition $\mathbf y_0$, where the dimension of the vector should be user-defined. ...
0
votes
1answer
538 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
votes
1answer
437 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: ...
1
vote
0answers
133 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 ...
4
votes
2answers
264 views

Simplifying the trace of a matrix expression

I have a long expression involving matrices that I derived using the NCAlgebra package. Can I simplify the trace of the expression? For example, say b is a scalar ...
1
vote
1answer
175 views

Hermite Normal Form in “columns” convention

After describing the Hermite Normal Form (HNF), MathWorld explains: The Hermite normal form for integer matrices is implemented in Mathematica as ...
0
votes
2answers
256 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 ...
0
votes
0answers
142 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
votes
1answer
161 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 ...
0
votes
1answer
217 views

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

Consider the following set of points in the 4D space: ...
1
vote
0answers
303 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 ...
5
votes
6answers
734 views

A matrix-vector cross product

I want to do a cross product involving a vector of Pauli matrices $\vec \sigma = \left( {{\sigma _1},{\sigma _2},{\sigma _3}} \right)$; for example, $\vec \sigma \times \left( {1,2,3} \right)$. ...
3
votes
1answer
169 views

Exploiting self-adjointness when changing basis

I am using Mathematica to analyze a real, self-adjoint matrix $H$ of the size $32 \times 32$, which comes from a physics problem. In the picture there is also a matrix $Q$ which commutes with $H$. I ...
1
vote
1answer
209 views

Partial row reduction of a matrix

I have an $m\times n$ matrix (presumably of full rank) with $m>n$, and I would like to row reduce it, but leave the last column unreduced; that is, I want to get output on the form $\pmatrix{ 1 ...
5
votes
4answers
677 views

How to find the index of a square matrix in Mathematica quickly?

Let $A$ be an $n\times n$ complex matrix. The smallest nonnegative integer $k$ such that $\mathrm{rank}(A^{k+1})=\mathrm{rank}(A^{k})$, is the index fo $A$ and denoted by $\mathrm{Ind}(A)$. I would ...
0
votes
2answers
1k views

large matrix eigenvalue problem

I need solve a very large complex matrix (not sparse and not symmetry) eigenvalue problem, e.g., 1e4*1e4 or even 1e6*1e6. How large dimensions of the matrix can Mathematica support? And, how about ...
2
votes
0answers
168 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 ...
4
votes
3answers
641 views

Compute the rank of a matrix with variable entries

Say I have a matrix like $$ M=\left( \begin{array}{c c c} x & xz & w-2x \\ wz^3 & xy & z \\ y^2-z^3 & x+w & z+x^5 \end{array} \right) $$ is it possible to ask Mathematica ...
1
vote
2answers
514 views

Matrix echelon/upper diagonal form

Is there a way to find the echelon form of a matrix in Mathematica? I see there is a function to find the reduced echelon form, RowReduce[], but I can't see ...
1
vote
2answers
224 views

Computing distance matrix for a list

Using functional programming in Mathematica, how can I compute a distance matrix for every element in a list of matrices... The distance would be computed between the item in the list and a "target ...
6
votes
0answers
163 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 ...
1
vote
2answers
908 views

Efficient ways to create matrices and solve matrix equations

I am attempting, for the first time, to use Mathematica to do some serious linear algebra. I would like to solve systems of equations of the form $$U_{n n'} f_{n'} = b_n.$$ I have an expression for ...
3
votes
2answers
1k views

Defining a non-commutative operator algebra in Mathematica

I am trying to develop a function(s) to do some commutator algebra to compute the enveloping algebra and ideals of a Lie algebra. For example if I have $SU(2)$ algebra generated by $L_i$ ($i=1,2,3$), ...
5
votes
2answers
248 views

Computing the sign of the real part of eigenvalues in a 3D linearized system with 3 parameters

So I have this dynamical system given by: $$ \left\{\begin{aligned} x' &= a(y-\phi(x))\\ y' &= x-y+z\\ z' &= -by \end{aligned}\right. $$ where $\phi(x) = \mu x^3 - \nu x$ and $a,b,\mu,\nu$ ...
4
votes
2answers
1k views

Gram Schmidt Process for Polynomials

I want to implement the Gram Schimdt procedure to the vector space of polynomials of degree up to 5, i.e. I want to find an orthogonal basis from the set of vectors $v=(1,x,x^2,x^3,x^4,x^5)$. The ...
4
votes
1answer
472 views

Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
7
votes
2answers
304 views

Why does my matrix lose rank?

I want to check the rank of a matrix for observability, but Mathematica loses a rank if the matrix contains very large numbers. Let's say my matrix is ...
0
votes
1answer
324 views

Why is EigenValues returning Root expressions?

This is the code I have: ...
0
votes
1answer
91 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 ...
3
votes
1answer
354 views

How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
0
votes
1answer
167 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 ...