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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Invoking WorkingPrecision slows down Eigenvalue calculation drastically?

Normally, obtaining eigenvalues of random numerical matrices is fast. For instance a generic result looks like ...
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0answers
31 views

Linear Programming Using Dual Simplex method

I want to solve an optimization problem using the Dual Simplex Method. Although Mathematica gives the result directly when I use the command Minimize but I want to ...
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0answers
46 views

Explicitly find a guaranteed factorization of large expression?

Consider the large expression LE defined in this file (involving only linearly independent functions), or in this file (linear interdependence present but slightly ...
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2answers
181 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
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1answer
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11
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1answer
120 views

Nearest Kronecker Product

Some people (see The ubiquitous Kronecker product by Van Loan) have worked on finding two matrices $\mathbf A$,$\mathbf B$ of specified size whose tensor product $\mathbf A\otimes\mathbf B$ is closest ...
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3answers
182 views

How to simplify symbolic expressions with KroneckerProduct

Having $X,Y$ being symbols for matrices, I was wondering if there is a way to simplify expressions like KroneckerProduct[X, X] + KroneckerProduct[-X, X] to ...
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1answer
105 views

Solve overdetermined set using Mathematica?

As shown below, this is a overdetermined system. Could you teach me how to find the optimized solution in Mathematica? I know it could be solved by the method of least square, but how to realize it in ...
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2answers
141 views

Solve a symbolic underdetermined Linear System

Dear StackExchange Community, I'm trying to solve an indeterminate linear system of equations, with $n+1$ variables and $n$ equations; therefore, I need to express all $n$ other variables a function ...
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2answers
57 views

LUDecomposition for non-square matrices

How do we go about finding the LUDecomposition for non-square matrices. When i try to input the standard LUDecomposition ...
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0answers
3 views

orthogonal vector from a vector and a matrix [migrated]

I have a vector $V1$, another vector $V2$, and a Matrix $M$, if I want $V2$ to be orthogonal to $V1$ I have to use Gram-Schmidt $$V2'=V2-\frac{V1.V2}{V1.V1}*V1$$ if I want V2 to be M-Orthogonal to V1 ...
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1answer
84 views

Orthogonalization is not commutative!

I get stuck into a problem: I am going to produce orthogonalized eigenvectors of a matrix and in any iteration. I shortened my question in the bellow line: Why do we face to different results of ...
3
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1answer
71 views

Easy way to solve a matrix equation for a matrix?

I have two sets of $10\times 10$ matrices $M1,M2,M3,M4,M5$ and $N1,N2,N3,N4,N5$ and I want to solve a set of equations for these matrices ...
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0answers
41 views

Mathematica package for explicit matrix representations of group generators?

While there are several packages that are capable of working with weights and roots (for example LieArt), I couldn't find any package that spits out explicit matrices for the generators, for example ...
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0answers
64 views

Choosing appropriate WorkingPrecision when solving numerical system of equations

Consider a linear system of equations, which is conveniently written as A.x=y. The matrix A has dimensions ...
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0answers
74 views

Suggestions for solving a large linear system

I have a system of $\approx 200,000$ linear equations in $\approx 40,000$ variables (with rational coefficients) and I would like to determine the dimension of the solution space, which I know to be ...
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0answers
105 views

MatrixExp of a complex matrix of size about 10000 by 10000 [closed]

I want to apply MatrixExp of a numerical, complex matrix of size about 10000 by 10000, and I also need high precision as I need to multiply several such matrices. ...
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0answers
66 views
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2answers
146 views

Difficulty using LUDecomposition

I'm having trouble using LUDecomposition with pivoting. I read the Mathematica help on this particular command, but I'm still lost. Take a matrix like: ...
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2answers
176 views

Why is mathematica eating a row from QRDecompostion

I'm attempting to calculate the QRDecomposition of the matrix: a= {{1,3},{0,5},{2,-8}} QRDecomposition [a] The answer mathematica gives me is: - Q which is a ...
2
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0answers
57 views

Derivative of vector dot product with respect to a vector

I have the expression: Transpose[gvecI, {2, 1}].x (m[1] + m[2]) gvecI and x are [3x1] ...
4
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2answers
50 views

Inputting values into the variables without having to input the matrix all over again

I'm practicing using LU decomposition on Mathematica. I am able to find the L & U matrices, specifically the variables. However, i find it tedious having to input the newly found values and form ...
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2answers
317 views

Given a set of four linearly independent vectors, how can I compute two additional linearly independent vectors?

I have four linearly independent vectors: $$ \left( \begin{array}{c} \left\{\frac{1}{2},\frac{1}{2},0,0,0,0\right\} \\ \end{array} \right)$$ $$ \left( \begin{array}{c} \left\{\frac{1}{2 ...
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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}]] ...
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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 ...
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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 ...
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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 ...
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2answers
194 views

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

Bug introduced in 8.0 or earlier and persisting through 10.2.0 Why can't Mathematica find the eigenvectors of this matrix? ...
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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. ...
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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 ...
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1answer
69 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 ...
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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 ...
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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
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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 ...
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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. ...
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0answers
48 views
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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 ...
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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 ...
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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 & ...
2
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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 ...
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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 ...
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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
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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 ...
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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
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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
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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
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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 ...
0
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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 ...