# 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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### Eigenenergies of a symmetric tridiagonal matrix [on hold]

we consider the time independent Schrodinger equation (TISH) where we want to calculate the first few instantaneous eigenergies. Discretizing space we get : So we can rewrite the TISH as, (where ...
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### Finding the magnitude a matrices [on hold]

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 ...
112 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, ...
311 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: ...
58 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: ...
64 views

### Aguilera-Perez Algorithm of $nD$ rotation matrix [on hold]

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: ...
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### Problem with Volume and Parallelepiped [on hold]

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] ...
97 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 ...
69 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: ...
118 views

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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 ...
548 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 ...
380 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? ...
56 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 ...
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### 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 $200 \times 200$ ...
123 views

### 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, ...
56 views

### 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 ...
50 views

### 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.
151 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 ...
101 views

### 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>>+(<&...
88 views

### 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 ...