# 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.

54 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 ...
63 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. ...
166 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. ...
79 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 ...
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 - ...
55 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 ...
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 ...
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 ...
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, ...
333 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: ...
61 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: ...
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] ...
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: ...
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

Can Mathematica generate symbolic expressions for gradients? For example, if $x_1$ and $x_2$ are two points, could I get Mathematica to generate expressions similar to the following? $\frac{\partial ... 1answer 102 views ### Efficiently compute this Table of NullSpace I have two$(2n,2n)$matrices,$A_1$and$A_2$, and I would like to compute $$\ker(A_1^p A_2^q -I)$$ for$p,q\leq 2n$. Both matrices are orthogonal and have exactly four non-zeros values on each ... 0answers 39 views ### Compiling LinearSolve with 2 complex matrices, possible bug Take two complex matrices depending on one variable, for example: ... 1answer 66 views ### Linear regression I have a sequence of data: data = {0.647888, 0.522495, 0.454224, 0.417054, 0.396816, 0.385798, 0.379799, 0.376532, 0.374754, 0.373786, 0.373259, 0.372972} How ... 1answer 75 views ### Mathematica will not run Arnoldi method while using NIntegrate This is simplified version of my real code: ... 1answer 53 views ### Orthonormalization of a set of vectors I know of the commands Orthogonalize[] and Normalize, but how can I combine them into one command that its output will be an orthonormalized list of the input vecotrs? Thanks in advance. P.S How to ... 0answers 28 views ### Using Arnoldi Method with Multiple Options I have a matrix with many complex eigenvalues, but I only need a few near a particular complex number. I am only looking at the imaginary parts, so I need the few closest on the imaginary scale to my ... 1answer 49 views ### Use of Inverse Matrix I solved a matrix as follows: {{0,1,1},{0,2,4},{0,3,9}}.{{0},{25},{20}} Resulting: {{45},{130},{255}} I tried to use an ... 1answer 51 views ### How can we do LDU decomposition modulo$p$? If we have an$n \times n$matrix, with all entries taken modulo$p$, how can we output the three matrixes in LDU decomposition, with all entries again modulo$p$? We can assume the input matrix is ... 1answer 68 views ### How to correctly calculate symbolic eigenvectors I give a minimalistic example of my problem: I have a matrix: m[a_,b_]:={{0,-a+b},{b,0}}; I define the eigenvectors as: ... 1answer 80 views ### Solving for five unknowns in a 3 x 3 matrix I know that matrix.Transpose[matrix] = IdentityMatrix[3] matrix = {{0.8111, 0.4867, -0.3244}, {a,b,0}, {c,d,e}} I tried ... 2answers 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$R^2$. ... 1answer 52 views ### Finding an Integer, Unimodular Matrix that connects two given matrices I have two symmetric, integer matrices,$K$and$K_2$which have the same determinant and the same signature (number of positive - number of negative eigenvalues). I want to find an integer valued ... 2answers 130 views ### How to plot a lattice (2D or 3D) given a basis I want a graphical picture of a lattice with basis such as$\{(1,1), (\sqrt{2}, -\sqrt{2})\}$. Does Mathematica already have a pre-made function that finds all linear combinations over$\mathbb{Z}$... 0answers 20 views ### 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 ... 2answers 274 views ### 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 ... 4answers 360 views ### Speedup matrix number multiplication Consider this simple matrix number multiplication: ... 1answer 60 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 ... 0answers 95 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$200 \times 200$... 1answer 128 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 ... 1answer 155 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, ... 1answer 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 ... 0answers 61 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$ais some large positive number. I ... 0answers 57 views ### Learning Mathematica for Math Majors [duplicate] I just downloaded Mathematica and I'm taking a course in Multivariable Calculus. I realize there is a lot of complexity to Mathematica and there are Many types of learning resources out there. I was ... 1answer 75 views ### Accuracy limitations of singular value decomposition? in the process of working on a physics problem I have found the need to use the singular value decomposition function built into Mathematica. I have encountered what seem to be limitations to the ... 0answers 26 views ### Ordering of Eigensystem in symbolic computations [duplicate] Suppose I have a symbolic 4x4 matrix for which I am finding the Eigenvectors and Eigenvalues. My question is whether Mathematica ... 1answer 72 views ### Plotting Invariant Manifolds of the Henon Map Given the following map: \begin{align} & x_{n+1}=-y_n+2x_n^2 \\ & y_{n+1}=\beta x_n \end{align} forβ \in (0,1)$,$x_n \in \mathbb{R}, y_n \in \mathbb{R}$(which is a one parameter version ... 0answers 47 views ### 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 ... 0answers 71 views ### 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 ...