# 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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### 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 <...
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### 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 ...
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### 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 ...
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### 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 ...
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. ...
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 ...
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 ...
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### LUDecomposition does not give the expected results [duplicate]

Check this example: ...
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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 ...
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 ...
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### 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 ...
253 views

### Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
82 views

### Simplifying normalized eigenvector, taking into account the freedom to choose phase

If we look at the simple matrix ...
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 ...
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### 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 ...
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 ...
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 ...
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,...
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### 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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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: ...
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 ...
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] ...
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 ...
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### 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 ...
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 ...
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 ...
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### 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:/...
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### Getting an approximate analytical form for eigenvalues of a matrix

I have a 20x20 matrix: ...
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### 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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### 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 ...
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 ...
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 ...