Questions on the linear algebra functionality of Mathematica.

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5
votes
2answers
651 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
3answers
574 views

How to solve an eigensystem faster?

I have a module that I need to call 1-10 million times in my program. Currently, it is taking several hours to run so I am hoping that I can cut down some runtime with your help. ...
5
votes
2answers
1k 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
3answers
1k views

Trying to simplify Root expressions from the output of Eigenvalues

I am trying to calculate eigenvalues of a sparse matrix with only two distinct non-zero elements, here Alpha and Beta, which are both negative reals. Mathematica returns some complex expressions with ...
3
votes
1answer
187 views
3
votes
2answers
507 views
2
votes
2answers
188 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 ...
2
votes
1answer
79 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
220 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: ...
2
votes
1answer
619 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 ...
1
vote
1answer
147 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
101 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
280 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 ...
1
vote
2answers
596 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
1answer
127 views

eigenvector bug also for matrix with numeric value [closed]

I just realize that probably there is a bug also in calculating the eigenvector of a matrix with numeric values (see here for bug in eigenvector calculation with symbolic value). In particular in my ...
0
votes
2answers
1k views

large matrix eigenvalue problem

I need solve a very large complex matrix (not sparse and not symmetry) eigenvalue problem, e.g., 1e4*1e4 or even 1e6*1e6. How large dimensions of the matrix can Mathematica support? And, how about ...