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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5
votes
1answer
116 views

Evaluating only one column of a $m \times m$ matrix without evaluating the matrix itself

Suppose I have f[x_] := SparseArray[{someRules}, {m, m}]; g[x_] := MatrixPower[f[x], k]; Would it be possible to evaluate only the $n$-th column ($n\neq m$) of <...
2
votes
0answers
76 views

Solve vs. LinearSolve - ill solutions using both methods [closed]

I'm wishing you a nice day. My question is related to this question previously asked by me, answered by PlatoManiac. Although I found a bug in his post I decided to leave his answer accepted and ask ...
4
votes
0answers
121 views

Eigenvalues FEAST method - performance is very variable

I am running the FEAST method option for Eigenvalues on sparse matrices of dimension around 500,000. I look for about 50 ...
3
votes
1answer
112 views

How to reduce an expression into user-defined variables?

In the following code, I define a set of matrices. Then, I define a function that calculates the commutation relation relation between these matrices ...
1
vote
0answers
60 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
4
votes
3answers
113 views

Find six vectors with rational entries under constraints?

Define six vectors v[i] with i=1,2,3...,6. Each v[i] is six dimensional and all entries in ...
2
votes
3answers
191 views

Eigenvectors of numerical matrix

I have a large numerical matrix whose eigenvalues are all distinct. In the documentation for Eigenvectors it says: For approximate numerical matrices m, the ...
0
votes
0answers
29 views

LUDecomposition does not give the expected results [duplicate]

Check this example: ...
1
vote
1answer
69 views

Invoking WorkingPrecision slows down Eigenvalue calculation drastically?

Normally, obtaining eigenvalues of random numerical matrices is fast. For instance a generic result looks like ...
2
votes
0answers
150 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 ...
3
votes
0answers
65 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 ...
10
votes
2answers
253 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
2
votes
1answer
82 views
13
votes
1answer
240 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 ...
6
votes
3answers
270 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 ...
2
votes
1answer
254 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 ...
2
votes
2answers
202 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 ...
1
vote
2answers
135 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 command,...
1
vote
1answer
100 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 ...
4
votes
1answer
93 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 ...
7
votes
0answers
88 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 ...
7
votes
0answers
81 views

Choosing appropriate WorkingPrecision when solving numerical system of equations [closed]

Consider a linear system of equations, which is conveniently written as A.x=y. The matrix A has dimensions ...
3
votes
0answers
124 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 ...
1
vote
0answers
119 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. ...
8
votes
2answers
188 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: ...
9
votes
2answers
249 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 ...
2
votes
0answers
81 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
votes
2answers
61 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 ...
6
votes
2answers
350 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 \sqrt{3}},-...
2
votes
0answers
125 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}]] ...
2
votes
0answers
73 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 ...
5
votes
1answer
241 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 ...
7
votes
3answers
389 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? ...
1
vote
1answer
113 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
87 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 ...
1
vote
1answer
104 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 &...
0
votes
0answers
42 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
48 views

Diagonal times dense matrix, high precision [closed]

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 ...
17
votes
1answer
313 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 and fixed in 10.3.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 ...
1
vote
0answers
30 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. https:/...
1
vote
0answers
65 views

Getting an approximate analytical form for eigenvalues of a matrix

I have a 20x20 matrix: ...
2
votes
0answers
84 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 ...
1
vote
1answer
115 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\end{...
2
votes
1answer
103 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 $b c+b f_2+b f_1+c f_2+c f_3+f_2^2+f_1 f_2+f_2 f_3+f_1 f_3$...
0
votes
0answers
102 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>>+(<&...
1
vote
1answer
146 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
34 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
58 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
103 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 ...