Questions on the manipulation of matrices in Mathematica.

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0
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0answers
36 views

Failure to evaluate functions of derivatives of Theta functions

I define a variant of the EllipticTheta function (multiplied by a constant factor) : ...
4
votes
3answers
335 views

Get Eigensystem to return orthogonal eigenvectors for Hermitian matrix

I have a Hermitian matrix, and I would like to get a list of orthogonal eigenvectors and corresponding eigenvalues. But when there are degenerate eigenvalues, sometimes Eigensystem/Eigenvectors ...
0
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0answers
86 views

Solving a system of equations involving partial derivatives for a wave

Before saying anything about the problem, I have checked "How to solve a system of partial differential equations?" yet it does not actually answers my question, as I have a 10x10 matrix to work on. ...
7
votes
3answers
610 views

How to estimate the matrix condition number in the 2-Norm?

The Mathematica documentation say it is possible to estimate the Matrix condition number in norm 1, 2, Infinity. But the 2-Norm raise a message. This is an extract from reference documentation ...
8
votes
7answers
293 views

Input a square matrix and return a list of the matrix entries read by antidiagonals

I have a square matrix: {{1,2,3},{4,5,6},{7,8,9}} and I want to get a list: {1,2,4,3,5,7}
1
vote
3answers
70 views

Form a matrix to have inequality elements

It looks like a silly question, but I could not find any answers online. Your help is greatly appreciated! Say I have two lists now. ...
0
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0answers
36 views

Does Mathematica support Laguerre Polynomials of Matrix Argument?

I am wondering whether Mathematica can also compute the Laguerre polynomials of matrix argument as the appear in multivariate statistics? For example, they appear in this paper here: ...
1
vote
1answer
70 views

Wrong generalized eigenvalues of large numeric matrices

I've been working on a toy model of a variational method of a Hamiltonian H with an overlap matrix S. The point is that when H and S are small enough, Mathematica gives the correct eigenvalues (≈ ...
1
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2answers
67 views

Insert an element to AdjacencyGraph

I'm not able to insert an element to mine AdjacencyGraph. I suppose that i should modify my AdjcencyMatrix: ...
5
votes
1answer
183 views

Largest matrix size supported by Mathematica 10

I have need to store large square matrices in memory, some times sparse, some times not. I have used up to $2^{15}$ by $2^{15}$ as my upper bound so far, and Mathematica has handled it even if it took ...
1
vote
1answer
56 views

Defining a matrix with the symmetry Transpose[A(q)]=A(-q)

I am trying to construct a symbolic matrix with the following property- $$ \left(D_{3\times3}(q)\right)^T = D_{3\times3}(-q) $$ Note that for $q\in \mathbb{R}$, $D(q)$ would be hermitian. So far i ...
0
votes
2answers
93 views

Obtaining the relations of variables using diagonal matrices

I know this is too an elementary question, but I am a pathetic newbie in mathematica and I cannot find any answer by googling. What I want is obtaining some relations of unknown variables using their ...
4
votes
3answers
210 views

How can I suppress zero or nonzero values in a matrix?

So, if I have something like: F[IdentityMatrix[3] // MatrixForm, 1] I'd like F[] to display: $$\begin{pmatrix} 1 & ...
5
votes
4answers
246 views

Replacing parts of a matrix

I'm a beginner to Mathematica and to writing scripts in general. I'm currently trying to write a code that will take any element in a matrix higher than a certain threshold value n and set it equal to ...
15
votes
2answers
399 views

Why is my data 10 times slower than random data when doing matrix multiplication

I have some data generated from some program, and it appears that matrix multiplication on these data are about 10 times slower than on some random data: ...
0
votes
0answers
99 views

How to speed up my code with constructing matrices

I have run this program for a long time to get the result for n = 2048(about 5hours) and no more result till now (can't run with n = 4096). I would know how to make it more efficient. Any help or ...
4
votes
2answers
168 views

Finding the Position of the Minimum Neighbor for Each Element in a Large Matrix

I have a large matrix ($6020\times 8452$), and I want to create a new matrix where the relative position of the minimum neighbor is each element in the matrix. For example, if I had the matrix ...
0
votes
0answers
21 views

'MatrixForm' problem [duplicate]

I prefer to use 'MatrixForm' because the form looks better in matrix manipulation. But my current problem is that after the use of 'MatrixForm', subsequent matrix calculations like 'Det' or 'Inverse' ...
3
votes
1answer
142 views

Calculate efficiently an expensive hermitian matrix

I want to compute a matrix $M_{pq}$, for which the calculation of each coefficients $M_{pq} = f(p,q)$ is an expensive function. I know that my matrix is hermitian, so that $M_{qp} = M_{pq}^{*}$. As a ...
3
votes
1answer
102 views

Making table of matrix product and efficiency

I want to make a table in which each element is a matrix product: ...
3
votes
1answer
179 views

Polar Decomposition

I'm new to Mathematica 10 (half-a-month user). I'm looking for a function of polar decomposition but for now I cannot find it. Can anyone tell me about related functions. Thanks in advance.
1
vote
1answer
59 views

Computation time depends on the matrix elements!

Consider these two lists of matrices, matrix and matrix2: ...
1
vote
1answer
88 views

Efficient method of raising matrix to a variable power?

I have a $2 \times 2$ matrix $A$, where each element is a 12th order polynomial in a parameter $a$. I need to raise this matrix $A$ to the $-t/T$ power, where $T$ is a known scalar (for this ...
2
votes
2answers
102 views

specified matrix query

can you tell me a way (best?) to get a matrix with i=N,j=N dimensions (quadratic) according to the following rules: variables: N , M, n the diagonal must contain zeros it must contain exactly M ...
4
votes
1answer
194 views

Table and memory efficiency

Consider these two types of creating matrices: Table[Table[i*j,{i,1,10}],{j,1,10}] Table[i*j,{i,1,10},{j,1,10}] I want to know if there is any difference ...
4
votes
1answer
182 views

Fast matrix multiplication in MMA and GPU

Matlab multiplies two 3000by3000 matrix around 0.18s faster than MMA. While for just a few matrix multiplications the speed difference is not important, it becomes crucial when I want to do those ...
0
votes
1answer
342 views

How to take transpose of a one dimensional vector? [closed]

Why the two followings giving me same output? At least one should give me a row vector and another should give me a column vector. MatrixForm[u = {1 , 1, -1, 1}] MatrixForm[v = {{1}, {1}, {-1}, ...
2
votes
1answer
355 views

Mean squared error of two matrices [closed]

I want to compare two matrices. For this I use the mean squared error between them with the following code mse[mat1_, mat2_] :=(mat1 - mat2)^2 // Flatten // Mean ...
5
votes
3answers
270 views

Multiplying block matrices

I have a 2*8 matrix A, and a 2*8*2 matrix B. So B[[1]] and B[[2]] are both 8*2 matrices. I need a neat way to multiply A by B so that the first list in the result is A.B[[1]] and the second list ...
2
votes
1answer
109 views

Rescaling and reorienting Matrix Plot axes

I have implemented a numeric Laplace Solver in C++ and am trying to graphically represent the validity of my method. I have outputted the grid from C++ and imported it into Mathematica to get the ...
0
votes
1answer
744 views

How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
1
vote
1answer
713 views

Computing the fundamental matrix and its monodromy matrix

Assume $\dot x(t)=v(x,t)$ is a $T$-periodic, with respect to $t$ dynamical system. That is: $x\in\mathbb R^n,\quad t\in\mathbb R,\qquad v(x,t+T)=v(x,t)$. Let $x_0$ be a smooth periodic solution in ...
3
votes
1answer
97 views

Print array with indices

Is there a single function that prints an array together with the indices? I know how to achieve this with Grid[{Range[n],array},Frame->All], but I vaguely ...
0
votes
0answers
38 views

parsed matrix not deleting elements in adjusted matrix

I have a matrix that has been parsed to delete certain rows and columns, as well as delete certain elements on the diagonal on the matrix. The problem is that it does this in theory when i take the ...
3
votes
2answers
104 views

How to reflect the entries of a square matrix about its anti-diagonal?

I need help with writing the mathematica code to reflect the entries of a square matrix about its anti-diagonal. I know to do it about the main diagonal using ...
0
votes
0answers
77 views

solving singular matrix [duplicate]

Hello I have a matrix that is singular, and i wanted to use linear solve to solve it but that doesn't work with mathematica. The matrix given as a list looks like this: ...
2
votes
1answer
99 views

Design matrix rank does not match

I'm attempting to fit a linear model and Mathematica returns the error message: "The rank of the design matrix 9 is less than the number of terms 10 in the model. The model and results based upon it ...
0
votes
1answer
91 views

Matrix form of complex numbers [closed]

Complex numbers have matrix form. But some 2x2 matrices while differ, represent the same complex number. To compare complex numbers one has to transform the matrices to the form \begin{pmatrix} a ...
3
votes
2answers
107 views

Help with building matrices

I am a complete beginner in Mathematica and I have a small problem. I have this three matrices (A,B and C) and with them I have to build larger matrix M which looks like this. What would be the ...
11
votes
3answers
4k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
2
votes
1answer
142 views

Computing with matrix differential operators

I am looking the achieve a working set of Mathematica functions that would allow me to take products, commutators, etc. of (2x2) matrix differential operators and apply them to vector-valued functions ...
0
votes
1answer
58 views

Why is there a seeming discrepancy with the expression Cofactor?

I was trying to find out the cofactors of a square matrix. Then I came across the command Cofactor in Combinatorica package. ...
5
votes
1answer
504 views

Matrix Rational Canonical Form

Is there a way to calculate the Rational Canonical Form of an $n\times n$ integer matrix using Mathematica? I have been perusing the documentation and web, but nothing so far.
0
votes
0answers
75 views

How to assign equation solutions to variables [duplicate]

I have 12x12 Matrix with which I have to solve the equation below: ...
1
vote
2answers
72 views

how to get continuation of square matrices with periodic diagonal band automatically?

I want write a function that can automatically analyze any square matrices with periodic band diagonals and give continuations of them. But I can't figure out an elegant way to do this. Suppose we ...
4
votes
1answer
141 views

CUDALink Error: A CUDALink kernel timed out?

I'm following the CUDALink tutorial [ http://reference.wolfram.com/language/CUDALink/tutorial/Introduction.html ] and everything is going fine until I get to the part that calls CUDADot on the ...
1
vote
0answers
104 views

Fast export of large numerical data

Edit It seems that the bottelneck is not due to eigen value problem. I will esit the question soon. I have a 6000by6000 matrix which I got after some calculations. I want to get the eigenvalues and ...
2
votes
1answer
68 views

Anyone knows the algorithm used by NullSpace function?

NullSpace function gives a list of vectors that forms a basis for the null space of the input matrix. When the rank of the input argument matrix $M_{m\times n}$ is ...
3
votes
2answers
108 views

Eigenvectors of large symbolic matrix

I have large symbolic matrix of order 32 x 32 given as ...