Questions on the manipulation of matrices in Mathematica.

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82 views

Inverting matrix of unknown size

I have a matrix that has a variable number of columns and rows (but it is always square). The matrix is: $$ \Gamma = \begin{bmatrix} \Theta & 0 & 0 & 0 & T & 0 & R_j \\ ...
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1answer
63 views

references in a nested matrix

I have a nested matrix n: ...
6
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0answers
285 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 ...
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0answers
64 views

Bug in PositiveDefiniteMatrixQ?

This seems like a bug in PositiveDefiniteMatrixQ to me: ...
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0answers
452 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 ...
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0answers
118 views

Discriminant of Characteristic Polynomial

I'm doing a calculation which finds the characteristic polynomial of a matrix with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 ...
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0answers
123 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 ...
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0answers
198 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 ...
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0answers
96 views

A math function similar to “LatticeReduce” for finding linear independent basis

We would like to ask a math function similar to "LatticeReduce" for finding linear independent basis. The input is a list of vectors $M=\{v_1,v_2,v_3,\dots\}$, with the following property: There is a ...
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0answers
147 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 ...
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0answers
71 views

Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
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0answers
75 views

How to sequentially select, from a large set of tuples (of matrices), those with a certain property

I'm interested in finding a computationally efficient way for selecting all tuples of matrices which have a certain property. The property I'm interested in is that I want the column sum, of f[the ...
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0answers
49 views

How to find a scaling parameter in matrix inversion process by MMA?

I simply would like to find the inverse of a given matrix $A$ by the iterative method $X_{k+1}=X_k(2I-AX_k)$ using $X_0=\frac{1}{\sigma_{max}^2}A^*$. An example is as follows ...
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76 views

What is the fastest way to obtain the eigenvalues of a Wishart matrix?

I would like a fast method of creating a sample of random numbers which corresponds to the eigenvalues of a Wishart matrix: For M>N the eigenvalues \lambda_i are given by the jpd Where $K_N$ is ...
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0answers
72 views

Define inverse for the custom operator

I want to define simple matrix algebra (inspired by the following posts: Block Matrix Algebra with Mathematica ; How to define custom operators ). I assume the funtion ...
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0answers
167 views

How to extract connected bipartite graph from incidence matrix

I'm trying to extract a connected bipartite graph Bconn from the a given incidence matrix B- I have a matrix representing a bipartite graph - the incidence matrix B (weighted or not is unimportant). ...
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0answers
142 views

Efficient submatrix swaps for large sparse matrix

I am implementing the 'swap' algorithm for a binary matrix to generate matrix permutations that maintain row and column totals. My problem is that my matrices are large and sparse (e.g., 19774 x 942, ...
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0answers
134 views

matrix with IF/THEN condition

How to generate all posible matrices with some conditions on the elements? I need to make for given $n$ all $n\times n$ matrices $A=(a_{ij})$ with three conditions: I. $a_{ij}=+1$ or $0$ or $-1$. ...
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282 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): ...
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230 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 (...
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87 views

Spectral Clustering

I am interested in the following question: How is it possible to check whether an algorithm is working properly? However, this question is too general for the post and I'd like to restrict attention ...
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44 views

how to solve an optimization problem in terms of matrices as the argument

How can I minimize an expression of the form a^T A a where a is a matrix. The following approach does not work if ...
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0answers
56 views

I see error messages when I use LogLinear Plot but not when I use Plot

I have written an application with Manipulate that plots the results of several calculations. What I find strange is that when I have my application use ...
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49 views

Geometric Transformation not working - degenerate points?

I've successfully used FindGeometricTransformation to project the simplex triangle onto the x-y plane: ...
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37 views

how to rewire the minimum number of edges in a disconnected bipartite graph, so to transform it in a connected one

Consider an incidence matrix A for a bipartite graph (Aij=1 if node i of group 1 and node j of group 2 are connected). A is not symmetric. Assume that A is disconnected or only weakly connected, i.e. ...
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133 views

3D isosurface plotting

I have a matrix of data of the form of 3 vectors R, Z, M1, M2, M3 ..., cylindric coordinates representing a measurement M of an axisymmetric hypersonic flow at the position R, Z (I don't measure along ...
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44 views

Extracting Coefficient Matrices from partial differential equations

I have a system of differential equations which are in the form Dt[a01,t] + u*Dt[a01,x] + v*Dt[a01,y] + w*Dt[a01,z] I have ten of these equations and my ...
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43 views

TableDirection in TableForm

I got confused about what does "the outermost dimension" and "the first dimension" mean in the document I snipped. Does it mean row or column?
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43 views

Find the values of parameters so that the matrix is symmetric positive definite

Good evening , I have a matrix 20x20 in symbolic form. The matrix depends on 5 parameters (a,b,c,d,e). I would like to get the interval of each parameters that ensures that the matrix S is symmetric ...
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57 views

How to compute variances from a matrix/table

I have created a matrix/table with an imported dataset. I want to know what the variance is for 3 values at a time but across 68 columns. I would like to do this in an automated way rather than 1 set ...
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25 views

Mathematica program for PLUR decomposition of a symbolic matrix using full pivoting

I wanted to ask if there is a Mathematica program for PLUR decomposition of a symbolic matrix M, such that M = P*L*U*R, using FULL (row and column) pivoting, and where R = reduced row echelon form of ...
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60 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
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92 views

Eigenvectors for a large symbolic matrix

I'm trying to compute the eigenvectors for a 42x42 symbolic matrix (with one variable) in Mathematica. I get the following error: Eigenvectors::eivec0: Unable to find all eigenvectors. >> and the ...
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584 views

Fastest way to create a NxNxNxN dimensional matrix

I have a function that outputs a complex number Func[x_,y_]:= blah blah; I have constructed a table of all possible values of this function. ...
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135 views

Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
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77 views

Back Linear Substitution

I have an equation set Ax=b and A(n*m),n<m . To lower down the dimension, I express some vars by other vars, which gives ...
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0answers
55 views

eigenvalues and eigenvectors without Root answers

I'd like to find eigen values and vectors of parametric 21*21 Matrix and i cant solve the root problem.please help me to find the answers without Root. My Matrix is: ...
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74 views

An error in converting matrix to quaternion

Here is an old quaternions package. There is a function named MatrixToQuaternion, References are here Matrix in that document is ...
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0answers
71 views

I need to draw a direction field and x1 vs t graph for the ode

I have written the following codes and i am able to get to the trajectory but not able to draw the direction field and x1 or x2 vs time plots. ...
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0answers
185 views

Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
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112 views

RowReduce : Record of all the row operations for RREF

I read "for what right-hand sides $b=(a,b,c)$ does $Ax=b$ have a solution", but that question pertains to solving for the unknown vector. I'd like a record of all of the row operations required to put ...
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97 views

Need Help with Output/Code Optimization Conparative Statics with System of Equations and Matrices

I have a system of equations (equilibrium conditions) and would like to evaluate how changes of exogenous variables affect the endogenous values. In step 1, I state the equilibrium equations and some ...
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98 views

Getting increased accuracy for roots of determinant

I have a matrix $a(\kappa)$ from which I am trying to determine $\kappa$ by using the equation $det(a(\kappa)) = 0$. The matrices I deal with are on the order of 100 X 100 to 500 X 500. Originally I ...
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47 views

Is there any way to stop calculation of unimodular matrix in HermiteDecomposition

I want to calculate Hermite normal form of a matrix. But I do not want the unimodular transformation matrix. Is there any way to stop the calculation of unimodular matrix? HermiteDecomposition ...
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117 views

How does Mathematica solve eigenvalues?

I believe mathematica uses some techniques beyond our book. According to the text book it is not possible to solve eigenvalues of which the matrix has not completely eigenvectors, or of those matrix ...
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0answers
86 views

Matrices and Upper / Lower Triangular Factorizations

Does anyone know (I have searched documentation, online and MathSource) if there are ways to coax out the following factorizations from Mathematica? $A = LU$, $LU$ factorization $PA = LU$, $LU$ ...
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51 views

Identify columns of a huge matrix just polynomially many rows chosen at random

I am interested in the following problem in combinatorics $\Cap$ Probability. Let $\lambda \in \mathbb{N}$ be a parameter. Consider a matrix of $2^\lambda$ rows and $2^\lambda$ columns. Each column ...
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325 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 ...
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162 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. ...