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.

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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: ...
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Find a condition that b must satisfy so that Ax=b has solution

I'm new to Mathematica, so I'm sorry if this is really simple. I am trying to find the condition that vector b must satisfy so that Ax=b has solution. I would like to learn a general method, but I'll ...
547 views

Mathematica Implementation of Householder’s Method

I typed the Householder code in this paper, which starts on page 7. The code is: ...
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General question about solving a large set of linear equations efficiently

In my research, I got a large set of linear equations, about 10 000 equations with more than 10 000 variables. It is not efficient to use "Solve", so does anyone know any way to solve the equations in ...
379 views

Can't find the eigenvectors of a simple 2x2 matrix

Bug introduced in 8.0 or earlier and fixed in 10.3.0 Why can't Mathematica find the eigenvectors of this matrix? ...
55 views

Fast Eigensystem calculation

I have a code which finds the eigensystem for a matrix H = H0 + x HInt, where x is a variable which turns on the interaction. H0 is diagonal, and HInt is a sparse matrix (with about 400 states, I hope ...
89 views

How does Mathematica compute the determinant of a matrix? [closed]

I have been trying to write efficient code for calculating the matrix determinant for some time now. I noticed last night that Mathematica is able to compute the determinant of a $200 \times 200$ ...
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Optimize a parametric matrix to get a lowest possible eigenvalue

This question is a followup of Plot the lowest eigenvalues of a parametric matrix Now I can get the lowest eigenvalue LowEign(t) of the matrix for a given t numerically. When I plot the LowEign ...
154 views

How do you solve a linear equation of matrices? [duplicate]

The function Solve works fine for scalars: In[]:= Solve[A x - x B + C == 0, x] Out[]= {{x -> -(C/(A - B))}} When using matrices however, ...
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Why can Mathematica compute numerical sums more efficiently when they are written as matrix operations?

Let $f(n)$ and $K(n,m)$ be functions such that the double sum, which we wish to evaluate numerically, $$\sum_{n=1}^a \sum_{m=1}^a f(n) f(m) K(n,m)$$ exists when $a$ is some large positive number. I ...
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Learning Mathematica for Math Majors [duplicate]

I just downloaded Mathematica and I'm taking a course in Multivariable Calculus. I realize there is a lot of complexity to Mathematica and there are Many types of learning resources out there. I was ...
66 views

Accuracy limitations of singular value decomposition?

in the process of working on a physics problem I have found the need to use the singular value decomposition function built into Mathematica. I have encountered what seem to be limitations to the ...
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Dealing with answers that have Root[ …] when finding an Eigensystem [duplicate]

This is a 3x3 matrix and I think it should solve for the expressions in terms of radicals. I am not sure what to do with this.
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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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Is Eigensystem::eivin message a bug?

I noticed that in the question Request for clarification of Eigensystem::eivn message the error message Eigensystem::eivn: Incorrect number 2 of eigenvectors for eigenvalue Root[<<14>>+(<&...
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How to get rid of # in answer (eigensystem)? [duplicate]

I was trying to find the eigensystem of the following matrix (act as if the second character is in subscript): \begin{pmatrix} 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \frac{-\...
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Ordering of Eigensystem in symbolic computations [duplicate]

Suppose I have a symbolic 4x4 matrix for which I am finding the Eigenvectors and Eigenvalues. My question is whether Mathematica ...
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Possible Bug in LinearSolveFunction with Sparse Vectors

Bug introduced in 5.0 and persists through 10.4.1 LinearSolveFunction is new in 5.0 Consider the following set of equations and corresponding variables: ...
67 views

Plotting Invariant Manifolds of the Henon Map

Given the following map: \begin{align} & x_{n+1}=-y_n+2x_n^2 \\ & y_{n+1}=\beta x_n \end{align} for $β \in (0,1)$, $x_n \in \mathbb{R}, y_n \in \mathbb{R}$ (which is a one parameter version ...
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Working with matrix

Considering the 3x3 matrix: m = {{0, -(I/Sqrt[2]), 0}, {I/Sqrt[2], 0, -(I/Sqrt[2])}, {0, I/Sqrt[2], 0}} How would I find its normalized vectors eigenvectors u_i ...
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Why does Eigenvalues work for a matrix $\{M\}$ but not $\{\{M\}\}$?

Suppose I have a matrix {{1, 2}, {3, 4}} which I'll call mat. In a blur of human error, I computed the eigenvalues of ...
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Is it possible to speedup these simple linear algebra operations

I'm trying to numerically solve some equations using splitting operator method. The solver I construct iteratively constructs a matrix and feeds it to LinearSolve. ...