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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15
votes
3answers
466 views

Compiling LinearSolve[] or creating a compilable procedural version of it

Earlier today I had a discussion with a representative at Premier Support about the 2 questions I've asked here over the past couple of days: Seeking strategies to deploy a function securely ...
10
votes
2answers
875 views

Is there any way to obtain an approximate inverse for very large sparse matrices?

I have a very large sparse matrix and I need to obtain its approximate inverse and save it as an sparse matrix too. Any of my efforts as could be seen in what follows fail for large n ...
14
votes
2answers
1k views

Higher order SVD

Does anyone know how to do a higher order SVD in Mathematica ? A good reference seems to be here http://www.sandia.gov/~tgkolda/pubs/pubfiles/SAND2007-6702.pdf but I don't understand their formalism ...
11
votes
1answer
520 views

Is there a built-in procedure for simultaneous diagonalization of a set of commuting matrices?

Given a set $\{A_1,...,A_m\}$ of $m$ commuting $N\times N$ diagonalizable matrices, it is known that there exists a basis of eigenvectors $\Lambda$ that simultaneously diagonalizes all the $A_i$. Is ...
11
votes
2answers
627 views

What's the most “functional” way to do Cholesky decomposition?

I can do Cholesky in a procedural style, such as: ...
7
votes
1answer
585 views

TensorContract of inverse matrix

Matrix inverse in mathematica If $A$ is an invertible $n \times n$ matrix, then $A\cdot A^{-1} = I$. To get this statement in Mathematica, you need the assumption ...
5
votes
3answers
877 views

Compute the rank of a matrix with variable entries

Say I have a matrix like $$ M=\left( \begin{array}{c c c} x & xz & w-2x \\ wz^3 & xy & z \\ y^2-z^3 & x+w & z+x^5 \end{array} \right) $$ is it possible to ask Mathematica ...
11
votes
3answers
596 views

Toggle visibility of elements in a plot

I have three simple graphs in one Plot. Now I am trying to make a button for each graph so you can hide or show it in the plot. Until now I was just able to make a checkbox with the Manipulate ...
9
votes
3answers
1k views

Has Mathematica a function to compute the Smith Normal Form?

The Smith normal form is a matrix that can be calculated for any matrix (not necessarily square) with integer entries. See Wikipedia for a more elaborate description. Has Mathematica a function to ...
9
votes
2answers
370 views

Speed up 4D matrix/array generation

I have to fill a 4D array, whose entries are $\mathrm{sinc}\left[j(a-b)^2+j(c-d)^2-\phi\right]$ for a fixed value of $\phi$ (normally -15) and a fixed value of $j$ (normally about 0.00005). The way ...
8
votes
2answers
181 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
5
votes
1answer
2k views

Solving a system of linear equations modulo n

I have a system of linear equations $$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$ What should I input (I'm using ...
3
votes
1answer
355 views

How can I get Mathematica to recognize equality of symbolic matrix expressions?

I have two matrix expressions: X.Transpose[T].Transpose[X] and X.T.Transpose[X] I want Mathematica to recognize that ...
11
votes
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 ...
9
votes
1answer
223 views

$3\times 3 = 6 + \bar{3}$ in Mathematica?

Can Mathematica handle this type of algebra, which is used very frequently in e.g. particle/nuclear physics? That is, I want to decompose a product of representations (in $SU(N)$ say) into irreducible ...
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 ...
6
votes
1answer
324 views

Is matrix multiplication automatically done in parallel in Mathematica 9?

In good old Mathematica versions (5.2, 6.0), matrix multiplication was automatically done in parallel. For example, on an 8-core machine, define two square real matrices: ...
5
votes
3answers
992 views

Solution for equation system with piece-wise defined functions

As I could swear this worked just yesterday, I am probably just doing something stupid here and I am sorry to bother you :) I am trying to find the point where a curve crosses a line. In this case, ...
2
votes
1answer
177 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
2
votes
2answers
418 views

Finding maximal sublist of linearly independent vectors

Given a list of vectors v = {v1, ..., vn}, which is the fastest way to find a maximal sublist of linearly independent vectors? I could add the vectors one by one to ...
8
votes
1answer
463 views

Efficiently Constructing Rank One Approximations for a Matrix using SVD

Suppose I have a $m\times n$ matrix $A$ (real for simplicity). Then SingularValueDecomposition[A] yields 3 matrices $U$, $\Sigma$ and $V$ such that $A = U\Sigma ...
7
votes
5answers
198 views

Selecting terms from a matrix

There are similar questions to this on the forum but none fit the purpose here: I would like to extract certain elements of a matrix depending on whether a factor is present or not, and create ...
7
votes
3answers
759 views

Composition of functions

I have a number of rotations computed by rot = RotationTransform[theta, point], and I would like to compose them to produce one function that is the composition of ...
6
votes
4answers
4k views

Computing eigenvectors and eigenvalues

I have a (non-sparse) $9 \times 9$ matrix and I wish to obtain its eigenvalues and eigenvectors. Of course, the eigenvalues can be quite a pain as we will probably not be able to find the zeros of its ...
5
votes
2answers
968 views

Can the CholeskyDecomposition function in Mathematica be made to work on non-symmetric matrices?

The CholeskyDecomposition[m] function in Mathematica requires a symmetric and positive definite matrix m. For instance, the ...
5
votes
1answer
2k views

How do I keep the right ordering of eigenvalues using Eigensystem?

I'm having an issue with the Eigensystem command. I need to diagonalize a bunch of 3 by 3 complex valued matrices, but more importantly, I need to keep the exact ...
4
votes
2answers
651 views

Solving a linear equation in Mathematica

This should be easy but I can't seem to find the right way to do it. I have an equation of the form $a x + b x + c y + a z + d z = 0$, and I'd like to solve for relations between the parameters ...
3
votes
6answers
137 views

What is the range of values $x$ for which $f(x)$ is higher than $k$ over a given domain?

What is the easiest way to answer the following question in Mathematica: Given a function $f(x)=y$, what is the range of values $x$ for which $y$ is higher than some number $k$ over the domain of $x$ ...
3
votes
1answer
83 views

Graphs Plotting Discontinuous

I'm trying to plot a graph from the eigenvalues of a matrix I created. The graph shows with discontinuities in it and I was looking for some feedback. Here's the code: ...
3
votes
2answers
260 views

Intersection of two vector spaces

Is there a simple way without having to manually compute the matrices and do LinearSolve to do the following? Assume I'm given two lists $l_1$, $l_2$ of vectors of the same dimension. I want a list of ...
3
votes
1answer
299 views
3
votes
2answers
642 views
3
votes
1answer
758 views

Linear Solve with Modular Arithmetic

I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
3
votes
3answers
1k views

Orthonormalization of non-hermitian matrix eigenvectors

When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
2
votes
1answer
399 views

Traces of products of Pauli matrices

Given a matrix $M$ of shape $2^L*2^L$, I would like to compute all the traces $\text{Tr}( M.(\sigma^{n_1}\otimes\sigma^{n_2}\otimes\ldots\otimes\sigma^{n_L})) $ for $n_1=1...4$, $n_2=1...4$, ..., ...
2
votes
1answer
99 views

How can we use RowReduce with a modulous AND variables?

We can use RowReduce with a field. For example, we state RowReduce[{{1,3,5},{0,1,2}},Modulous->23] ...which then returns: ...
2
votes
1answer
269 views

How to obtain a Symplectic 4×4 matrix?

I have a problem in obtaining a $2n \times 2n$ Symplectic matrix $T$, with $n=2$. I couldn't find a direct command in Mathematica to achieve this. Conditions: ...
1
vote
1answer
149 views

Transform linear system into a matrix form

I have a system of linear equations in variables $A_n$ of form: $$ \sum _{k=-K}^K h_k A_{n-k} J_{n-k}\left(\frac{(1-i) \text{$\eta $Sqrt}(n-k)}{\sqrt{2}}\right)+A_n\left(\frac{(1-i) \eta ...
1
vote
0answers
93 views

Request for clarification of Eigensystem::eivn message

What causes the problem of "two eigenvectors associated to one single multiplicity eigenvalue" that I am experiencing? After several transformations to simplify an unwieldy matrix, I end up with the ...
1
vote
1answer
203 views

What is most efficient way to convert system of equations to collection of functions?

I have the type of system M.x = b, where M is a known matrix and b is a known vector. M contains many parameters, call the entire parameter set 'a', so M => M[a]. I want to be able to efficiently ...
1
vote
0answers
133 views

(Symbolic) LinearSolve is slower/different after upgrading to Mathematica 9

Yesterday I upgraded from mathematica 8.0.4.0 to 9.0.1.0. Trying to run the same notebook I used many times before, it takes ages to evaluate a symbolic (linearsolve) expression which before was ...
1
vote
2answers
959 views

How to Solve or LinearSolve $A = I$ matrix equation?

I'd like to solve this equation for $A = B$ where $B = I$, which represents 3 systems of 3 linear equations, for $a, b, c, d, e, f$, without writing LinearSolve 3 ...
0
votes
0answers
47 views

CharacteristicPolynomial returns 0

I have the following matrix. ...
0
votes
1answer
81 views

Why `FindMaximum` doesn't work in my example

Consider the following function ...