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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2
votes
0answers
50 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
1
vote
0answers
51 views

Addition of sparse array objects [duplicate]

Bug introduced in 9.0.0 and fixed in 10.0.0 I have been having some trouble with the addition of large (but very sparse) matrices using SparseArray. Here is the simplest example to illustrate the ...
2
votes
0answers
41 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
10
votes
2answers
3k views

Badly conditioned matrix (General::luc)

With some matrices, I am receiving the following message: ...
7
votes
3answers
741 views

How to estimate the matrix condition number in the 2-Norm?

The Mathematica documentation says it is possible to estimate the matrix condition number in norms 1, 2, and ∞. But the 2-norm raises a message. This is an extract from reference documentation ...
1
vote
0answers
47 views

How to remove parts of an expression

I have an expression where terms Transpose[R].R appear. R is a matrix with the property Transpose[R].R=IdentityMatrix[3]. How ...
5
votes
1answer
103 views

Distribute transpose on matrix multiplication

I need to do the following: Transpose[A.(B+C)]=Transpose[B].Transpose[A]+Transpose[C].Transpose[A] How should I do this in mathematica? So far mathematica does ...
33
votes
2answers
841 views

eigenvector bug?

Bug introduced in 7.0.1 or earlier and fixed in 10.0.0 I have a fairly simple $3\times3$ complex matrix, $$ M=\left( \begin{array}{ccc} \frac{7}{2}-\frac{i}{2} & -1+i & \frac{1}{2}+\frac{5 ...
1
vote
1answer
63 views

Transposition of state space form of a transfer function

How can I transpose the output of state space model in Mathematica? trying the following code would transpose the top right symbol s instead of the matrices. ...
0
votes
1answer
71 views

Find all degenerate eigenvalues of a cubic equation

I have an equation that is cubic in w. The three solutions correspond to bands in a bandstructure, and are a function of wavevector ...
0
votes
3answers
181 views

Calculating eigenvalues of a large matrix takes a long time

I have a tridiagonal matrix (1000×1000) with each element equal to $1$ except {n, n} = 2. It takes 8 hours to give me the eigenvalues?!! Here is the code I used: ...
1
vote
1answer
68 views

Handle matrices and vectors with general dimension

I have a matrix of $n \times n$ dimension: $$ K - \omega^2 M = \begin{pmatrix} 2\omega_0^2 - \omega^2 & - \omega_0^2 & 0 & \cdots & 0 \\ - \omega_0^2 & 2\omega_0^2 - \omega^2 ...
8
votes
3answers
657 views

Visualization of matrix transformations

I define the "matrix transformation" here as follows: $\left[ \begin{matrix} x_1' \\ x_2' \\ \end{matrix} \right]=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} ...
0
votes
0answers
40 views

Signage of eigenvector [duplicate]

I am comparing eigenvectors generated from mathematica to matllab. It seems signage of eigenvector generated from Mathematica is opposite from what is generated from matlab. Can anybody review and ...
1
vote
0answers
35 views

Diagonal times dense matrix, high precision

I have a fixed dense matrix M of high precision numbers, say 40 by 40 and precision 40. Then I have a variable vector v of the ...
15
votes
0answers
201 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 array with symbolic ...
1
vote
0answers
28 views

Function to be used for spectral decompostion of matrix [duplicate]

Can anybody please help in finding out what is best way to do spectral decomposition (or Eigen decomposition) of the matrix. The details of Eigen decomposition can be found in attached link 1. ...
2
votes
0answers
62 views

MatrixRank of a large but sparse matrix

I want to find the rank of a very sparse, quite rectangular matrix mat, but I'm running out of RAM (I have 16 GB) if I try to use ...
22
votes
2answers
1k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
4
votes
3answers
286 views

What is the best way to write a polynomial in the Bernstein basis?

The Bernstein basis of polynomials of degree $n$ is the set of polynomials of the form $$\binom{n}{k} t^{n-k}(1-t)^k$$ where $0 \leq k \leq n$. What is the best way to transform a given polynomial ...
3
votes
1answer
561 views

Specific Mathematica algorithms, for example LU Decomposition

Where I can find detailed information on algorithms used by Mathematica, especially for numerical methods. The Manual doesn't seem to iclude specifics in most cases. For example I get a different LU ...
1
vote
1answer
90 views

Matrix multiplication for higher dimensional matrices [duplicate]

I have a matrix like this (myb1): I would like to get the matrix multiplication of each of the submatrix to itself. For example the first 2x2 matrix $\begin{bmatrix}1 & 2\\1 & ...
0
votes
0answers
48 views

Compilable function with the functionality of SingularValueList

I'm doing something that involves finding the singular values of a lot of matrices. Basically I need to find singular values of $n$ matrices of dimension $n\times n$, where $n$ is as large as ...
2
votes
1answer
74 views

Expand a product of operators

Lets suppose I have a family of operators $f_i$, and unknown c-numbers $a,b,c$. I want to expand such products: $(f_1+f_2+c)(f_3+f_2+b)$ into $b c+b f_2+b f_1+c f_2+c f_3+f_2^2+f_1 f_2+f_2 f_3+f_1 ...
4
votes
1answer
239 views

How to draw a tropical surface?

By definition, a tropical surface in $\mathbb R^3$ is the set of points $(x,y,z)$ where the maximum $f=\max(f_1,f_2,\dots,f_n)$ is attained at least twice, here $f_i$ stand for some linear functions ...
0
votes
0answers
54 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 ...
1
vote
1answer
65 views

Multiplying three matrices does not give expected form [closed]

I'm having lectures on analytic geometry. I've learned that there is an associated matrix multiplication for a quadratic form: $\quad \quad \left( \begin{array}{ccc} x & y & 1 \\ \end{array} ...
2
votes
0answers
32 views

How to get simultaneous eigenvectors of commuting matrices? [duplicate]

So let's say there are two square matrices A and B that commute (AB-BA=0). This implies that there must exist some complete set of vectors that are eigenvectors of both A and B. Is there any way to ...
1
vote
0answers
47 views

Does a matrix need to be rationalized when calculating MatrixExp? [closed]

I have a sparse matrix, L, and need to calculate its exponential, MatrixExp[L t], where t is ...
1
vote
1answer
55 views

Mathematica computes wrong eigenvectors? [closed]

I have a matrix M = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, b}, {0, 0, -b, 0}} that I want to diagonalize. So far, I always used the following and it worked, but ...
0
votes
1answer
124 views

Traces of products of Gell-Mann matrices in FeynCalc

I am working on an assignment in FeynCalc and I need to evaluate traces of products of two commutators of Gell-Mann (SU(3)) matrices, i.e. I need to calculate the ...
1
vote
0answers
41 views

reset the value of a variable [closed]

Folks, I have a problem in populating a matrix without overriding the values. After performing computations for various values for j, I want to store these values in following matrix. Here is the ...
3
votes
1answer
88 views

Solve an eigensystem faster and eliminate Root[…] from the solution

I have a symbolic, 2-parameter, 8x8 matrix to solve, but Mathematica takes something like 20 minutes to solve it and returns a very large output containing expressions of the form ...
0
votes
0answers
55 views

Null space of a stochastic matrix [closed]

I want to calculate NullSpace of a matrix m - IdentityMatrix[n]. Normally I would do it with ...
4
votes
2answers
121 views

Pauli matrices — simplify expressions without printing out the raw matrix

Squaring a Pauli matrix results in the identity matrix. These bits of documentation (weakly, to a Mathematica-newbie like me) imply that some algebraic identities that link the Pauli matrices ...
2
votes
2answers
2k views

Is there a built-in function to find the adjoint of a matrix?

I've been looking for a function that helps me get the adjoint matrix o a given one, I found that you can get the cofactors of a matrix but only by using the "Combinatorica" package, which I couldn't ...
10
votes
1answer
426 views

How get eigenvectors without phase jump?

I'm using Eigenvectors to get the eigenvectors for some matrixes, but the eigenvectors seems to have some phase jump. Here is an example: Say we have a 2 by 2 ...
0
votes
0answers
34 views

Why is there a different eigenvector for the same matrix? [duplicate]

I have a matrix that depends on two variables x and y. Matrix[x,y] When I make x=-.25*(1 - 1/3) + .25*(1/3) + .25 y=0 I ...
1
vote
1answer
160 views

Efficient algorithm to generate a basis for exact diagonalization

The problem is described as follows: I need to generate a basis(matrix) in lexicographic order. For two different basis vector $\{n_1,n_2,\cdots,n_M\}$ and $\{t_1,t_2,\cdots,t_M\}$, there must exist ...
7
votes
5answers
1k views

Check if a matrix is Positive Semidefinite

I have a question concerning the check whether a given matrix is positive semidefinite or not. In mathematica the function PositiveDefiniteMatrixQ[m] tells me ...
12
votes
2answers
949 views

Find the eigenvector associated with the smallest eigenvalue, not smallest in magnitude

I am trying to find the eigenvector of a $20000 \times 20000$ sparse matrix associated with the smallest eigenvalue. I realized that the smallest eigenvalue might be negative; for example, if the ...
13
votes
1answer
421 views

Why is MainEvaluate being used when LinearSolve can be compiled?

According to this question LinearSolve can be compiled. However, CompilePrint[] shows a call to ...
0
votes
0answers
56 views

Normalized, symbolic Eigenvectors without abs(), sign() etc

I'm trying to compute the normalized eigenvectors of a matrix M = {{0, 0, 0, 0}, {0, 0, M5, 0}, {0, M5, 0, M4}, {0, 0, M4, 0}} If I try Normalize ...
4
votes
1answer
177 views

Eigenvalues of matrix not giving imaginary parts

This might be a very simple problem, but I can't seem to figure out why I am getting this. I am trying to find the eigenvalues of the matrix: ...
2
votes
1answer
423 views

Matrix exponential MatrixExp[] vs Sum[MatrixPower[]] doesn't match?

I might be an idiot, but I cannot get the manual expansion of $e^{At}$ to match the MatrixExp[A t] result. For example, I have the following: ...
2
votes
2answers
117 views

Reordering numerically calculated eigenvalues assuming smooth dependence on a parameter

As was discussed in a different question here on SE (link) if you compute eigenvalues numerically of a matrix which depends on a parameter y, the resulting plot of ...
27
votes
1answer
3k views

Simplify matrix algebra

I'm trying to simplify some matrix linear algebra, for example, simplify $$\big(a1\times(A1\cdot A2)\big)\cdot\Big(a2\times A3\cdot A4+(a3\times A5)\cdot(a4\times A6)\Big)^{T}$$ where lower case ...
5
votes
1answer
543 views

Generating random symmetric matrix

Suppose first that I want to generate a matrix whose elements are independent and identically distributed (i.i.d.) with distribution dist. This is easy: ...