Questions on the manipulation of matrices in Mathematica.
3
votes
2answers
386 views
Can RowReduce work in this matrix?
The matrix $Q$ with dimensions $n\times2*n*m$ is structured by
$$Q=[B|AB|\cdots|A^{2*n-1}B]$$
where $Q$ is an augmented matrix built from a $3\times3$ matrix, $A$, and a $3\times2$ matrix, $B$.
I ...
4
votes
1answer
124 views
Sorting a matrix alphanumerically
Somewhat related to Sort matrix by columns and rows without changing them, but more general.
I'd like to sort a square matrix (a 3 by 3 in my case, but surely the general solution will treat any), ...
2
votes
1answer
392 views
6
votes
0answers
231 views
Inverse of a large sparse Hermitian block matrix
I am looking for a method (if it exists) for the inverse of a large sparse Hermitian block matrix.
The off diagonal sparse matrices, named δ are 4x4, and they have ...
6
votes
0answers
227 views
MMA implementation of Earth Movers Distance?
Has anyone implemented in MMA the Earth Mover's Distance (EMD)? A concept dating back to Monge 1871, used to compare histograms and images, e.g., the CIEDE2000 Color Difference algorithm. Yossi ...
3
votes
0answers
85 views
Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?
If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
3
votes
0answers
65 views
Is it possible to lower the bitwidth of (floating point) numbers?
The answer to this question will most probably be a definite no. Nevertheless, I would like to know whether it is possible to represent reals in the memory on less than the standard 32 or 64 bits ...
3
votes
0answers
74 views
How to accelerate updating some parts of sparse matrices?
I am trying to update some parts of an specific matrix as rapidly as possible. In what follows, I first set up the basics things that I want to use
...
3
votes
0answers
157 views
Mathematica Complains about Non Symmetric Covariance matrix, when it's not the case
I was doing some fitting with Mathematica7 using NonlinearModelFit. It's quite long the program to do the fit and that's why I am not displaying here ...
It goes ok, and I can get the fit parameters ...
2
votes
0answers
67 views
Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)
I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
1
vote
0answers
75 views
1
vote
0answers
89 views
Dynamically filling matrix with a[[n,m]] = 1/a[[m,n]]
I'm building a square matrix, with 1s on the diagonal and elements in U the inverse of elements in L, which are random integers drawn from the sequence 1, ..., 9. Given the nature of the problem I ...
1
vote
0answers
172 views
Matrix algebra vs. PrincipalComponents and Varimax/Oblimin
Using matrix algebra I can calculate loadings and scores from the covariance matrix (data matrix is column centered):
...
1
vote
0answers
173 views
Can mathematica simplify an expression setting simplified answer equal to zero?
Basically I want to reduce something like:
Subscript[P, 4] - Subscript[P, 5] == Subscript[R, 4, 5]* Subscript[i, 4, 5]
when only one of them is known (...
0
votes
0answers
54 views
Sudden increase in computation time for similar computations
I'm doing some numerical simulations on a physical system. In the most simplest form I have now the following:
...
0
votes
0answers
96 views
Solve equations real and imaginary part separately
For my system of equations, the procedure described in Solving complex equations of using Reduce works no more. How can I separate the real and imaginary part of ...
0
votes
0answers
81 views
Defining and Solving Systems of Equations Using Matrix Tables
I've defined a system of equations, but I been unable to get Mathematica to solve for the individual variables created by matrix tables.
...
0
votes
0answers
119 views
6x6 matrix NullSpace
I'm working with a 6x6 matrix. Whenever I try to find the NullSpace and FullSimplify it, I get the error
No more memory ...
0
votes
0answers
361 views
Jacobi eigenvalue and eigenvectors algorithm
Suppose we have a symmetric matrix with dimensions n x n. I need to find the eigenvalues and eigenvectors of this matrix using the Jacobi method. I wrote this code:
...
0
votes
0answers
132 views
How Simplify and Assume can be combined on matrix products?
What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
