Questions on the manipulation of matrices in Mathematica.

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1
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2answers
132 views

LUDecomposition for non-square matrices

How do we go about finding the LUDecomposition for non-square matrices. When i try to input the standard LUDecomposition ...
0
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1answer
88 views

Eigenvalues and Eigenvectors Order [duplicate]

Say I have a list of eigenvalues and eigenvectors produced from a matrix $M$ using the command {eig1,eig2}=Eigensystem[M], which will return the eigenvalues with ...
0
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1answer
37 views

Variable Definitions and Random Numbers [closed]

I have currently created the following matrix: m={{RandomReal[{0,1}],RandomReal[{0,1}]},{RandomReal[{0,1}],RandomReal[{0,1}]}} In other words, a $2 \times 2$ ...
0
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0answers
21 views

Matrix Multiplication and Product [$f$, {$i$, $i_{min}$, $i_{max}$}] [duplicate]

I tried the command Product[f, {i, i_min, i_max}], where $f$ is a matrix here, as a shorthand for a product of arbitrarily many matrices with elements parametrized ...
3
votes
1answer
85 views

Evaluating the product of a matrix sequence [duplicate]

I want to compute $$ \prod_{i=1}^n A_i = A_1 A_2 \cdots A_n $$ where every $A_i$ is a square matrix. When I execute ...
3
votes
1answer
112 views

updating matrix elements based on a condition

I am (still) fairly new to Mathematica and trying to perform some operation on the matrix elements, say for the matrix ...
14
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2answers
247 views

Fastest way to sum the upper triangle

I feel like this is an recurring question: if there's a symmetric matrix whose diagonal is not all 0, how could I get the sum of the part of it that's above the diagonal as fast as possible? Small ...
1
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1answer
71 views

Matrix issue with NDSolve

I am solving a differential matrix equation with NDSolve. ...
6
votes
2answers
197 views

improving sequence dot operator for matrix rows and plot of Norm-imaginary

I have written a code to Dot a row (conjugate of that) of mm to the next one: ...
6
votes
2answers
382 views

delete zero rows in a matrix

If there is a matrix with some of its rows equal to zero: (its zero rows are randomly distributed and does not have an ordered arrangement): same as: ...
1
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1answer
99 views

Orthogonalization is not commutative!

I get stuck into a problem: I am going to produce orthogonalized eigenvectors of a matrix and in any iteration. I shortened my question in the bellow line: Why do we face to different results of ...
4
votes
2answers
136 views

Reading from a file: complex number with small imaginary part

I'm trying to read a matrix from the next file: 1+1e-18i 24 42 23.43e-23i using u=Import["file.dat","Table"]; and then find, ...
2
votes
3answers
98 views

How to compare and remove x-coordinates (and the associated y-coordinates) that are less than previous x-coordinates?

I am using Mathematica version 9.0 and am trying to compare and remove x-coordinates, and the associated y-coordinate, that are less than previous x-coordinates. Below is an example using sample data. ...
1
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0answers
89 views

Simplest use of transpose given a vector and a matrix [closed]

Suppose that I have: x = {1, 1}/Norm[{1, 1}]; A = {{1, 2}, {2, 1}}; What is the simplest way of calculating $x^T A\ x$? And are there symbols on any of the ...
1
vote
1answer
77 views

Issue with Differentiation over a tensor

I am new user in Mathematica. I am working with liquid crystal theory, and one of the notation there is the tensor: $ \Pi_{ij} = \frac {\partial {F_{el}}} { \partial ( \partial {n_i} / \partial { ...
3
votes
1answer
52 views

Saving Dot-ed eigenvectors in a special comparison

We have produced a 4*4 matrix in any iteration containing nx from 0 to 2 by steps of 0.5. and in any iteration we have saved sorted orthogonalized-eigenvectors based on their eigenvalues with this ...
1
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0answers
118 views

MatrixExp of a complex matrix of size about 10000 by 10000 [closed]

I want to apply MatrixExp of a numerical, complex matrix of size about 10000 by 10000, and I also need high precision as I need to multiply several such matrices. ...
0
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0answers
59 views

Solving matrix optimization

I have the following problem. Let $X_1, X_2, \cdots, X_k$ are $n \times n$ Hermitian matrices (need not be positive) given. Let a $n \times n$ positive matrix $A$ is given such that $Tr(A.X_j)<0$ ...
8
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2answers
183 views

Difficulty using LUDecomposition

I'm having trouble using LUDecomposition with pivoting. I read the Mathematica help on this particular command, but I'm still lost. Take a matrix like: ...
9
votes
2answers
238 views

Why is Mathematica eating a row from QRDecompostion

I'm attempting to calculate the QRDecomposition of the matrix: a = {{1, 3}, {0, 5}, {2, -8}} QRDecomposition[a] The answer ...
1
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1answer
69 views

calculate relationship between cause and effect (rows/columns/delta etc.) on tableform

I tried to enter this Excel (on the right of the picture) information to program. following these codes has been used: ...
5
votes
1answer
105 views

Efficient upsampling of multidimensional array

I would like to efficiently upsample a multidimensional array. It's a 5000*5 matrix where each element is a submatrix 12*12 and it is that 12*12 matrix I want upsampled (to 24*24). The upsampling ...
1
vote
1answer
81 views

Pure “Select” function over matrix

I have several lists of tuples in the following shape: l1 = {{1, 134}, {2, 314}, {3, 164}} I do want to select, from each list, list elements fulfilling a ...
4
votes
2answers
128 views

Factor out the scalar multiplier for the dot product of 2x2 matrices

If yy and zz are 2x2 Hermitian matrices, is there a way that I can mark them (with a property?) as Hermitian so that Mathematica can assume that it can factor out and simplify scalar multipliers from ...
1
vote
1answer
66 views

Sort and Save Matrices Eigenvectors to a Larger Matrix

We are going to sort and save all orthoginalized-eigenvectors of 4*4 random matrices (produced in any iteration) to a larger matrix such as storagematrix. Since, produced random matrices are 4*4, ...
2
votes
0answers
114 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
0
votes
1answer
109 views

Element assignment in matrix function

I have to define a function of two variables that yields a high dimensional matrix, with each entry containing a scalar function, that uses its coordinates in the matrix as input. like this: ...
1
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0answers
82 views

How do I diagonalize a matrix? [closed]

How do I diagonalize the following matrix: ...
1
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0answers
59 views

How to remove parts of an expression

I have an expression where terms Transpose[R].R appear. R is a matrix with the property Transpose[R].R=IdentityMatrix[3]. How ...
5
votes
1answer
236 views

Distribute transpose on matrix multiplication

I need to do the following: Transpose[A.(B+C)]=Transpose[B].Transpose[A]+Transpose[C].Transpose[A] How should I do this in mathematica? So far mathematica does ...
1
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5answers
171 views

Do not expand matrices in Mathematica calculation

Here is an example of a problem I'm having. Consider that I have defined: omega={{p[t]},{q[t]},{r[t]}} x={{a},{b},{c}} R={{1,2,3},{4,5,6},{7,8,d}} What I would ...
7
votes
3answers
372 views

Can't find the eigenvectors of a simple 2x2 matrix

Bug introduced in 8.0 or earlier and fixed in 10.3.0 Why can't Mathematica find the eigenvectors of this matrix? ...
1
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1answer
87 views

Calculating a multiplication of large number of matrices takes a long time [duplicate]

I have a multiplication of matrices, say M1.G1.M2.G2.....Mn.Gn, here n may reach 100. M and G are 4 4 matrices and their elements are function of s. Mathematica takes so long to perform this ...
4
votes
0answers
138 views

How can I force the use of sparse diagonalization methods?

When I evaluate the Eigenvalues function on a very large (e.g. 2^16 x 2^16) sparse matrix, Mathematica says something like: Because finding 65536 out of the ...
0
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0answers
40 views

Dot production associated with comparison process of different matrices eigenvectors

With thanks to Guess who in the link module using.. We created functional 5*5 matrices: ...
1
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1answer
108 views

Transposition of state space form of a transfer function

How can I transpose the output of state space model in Mathematica? trying the following code would transpose the top right symbol s instead of the matrices. ...
0
votes
2answers
102 views

Matrixform ndsolve for mobile robot dynamic equations

Error is: NDSolve::ndsdtc: The time constraint of 1.` seconds was exceeded trying to solve for derivatives, so the system will be treated as a system of differential-algebraic equations. You ...
1
vote
1answer
82 views

multiplication of 4*4 matrices whose elements are function of x and y [closed]

I have a matrix 4*4 M whose elements are a function of x and y. I would like to multiply this matrix for different values of x and y, say M[1,1].M[2,2]......M[n,n]. How I can do it?
2
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1answer
95 views

Problem with NDSolve and Sign

If c1 cnd c2 are zero, the code responds very well; but if one of c1 or ...
2
votes
1answer
96 views

Extract Transfer Matrix from TransferFunctionModel

I have a MIMO transfer function model, and I'd like to know how to perform arithmetic on this model. For instance, to see the difference between two systems' outputs for arbitrary inputs, I'd like to ...
1
vote
1answer
99 views

Handle matrices and vectors with general dimension

I have a matrix of $n \times n$ dimension: $$ K - \omega^2 M = \begin{pmatrix} 2\omega_0^2 - \omega^2 & - \omega_0^2 & 0 & \cdots & 0 \\ - \omega_0^2 & 2\omega_0^2 - \omega^2 ...
5
votes
3answers
285 views

Huge matrices crashes in Mathematica

I have a matrix of data ~(70,000x70,000). I am searching connection between these data points. I use euclidean distance for that purpose. If it is less than my threshold (that means they have ...
1
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0answers
47 views

Diagonal times dense matrix, high precision [closed]

I have a fixed dense matrix M of high precision numbers, say 40 by 40 and precision 40. Then I have a variable vector v of the ...
6
votes
3answers
252 views

On a strange pattern of triangular numbers in Ulam's spiral

In this MSE post, user GeMir noticed that, where the green dots are the triangular numbers, $$T_n = \frac{n(n+1)}{2} = 1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,\dots$$ in the Ulam spiral ...
17
votes
1answer
307 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 and fixed in 10.3.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 ...
1
vote
1answer
80 views

Displaying a matrix with integral entries

I have a matrix nxn with coefficients a[i,j] like: a[i,j]=NIntegrate[T[r], {r, -le, le}] - NIntegrate[T[r] Abs[r]/le, {r, -le, le}] I can solve the matrix but I ...
1
vote
0answers
30 views

Function to be used for spectral decompostion of matrix [duplicate]

Can anybody please help in finding out what is best way to do spectral decomposition (or Eigen decomposition) of the matrix. The details of Eigen decomposition can be found in attached link 1. ...
1
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0answers
64 views

Getting an approximate analytical form for eigenvalues of a matrix

I have a 20x20 matrix: ...
2
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0answers
80 views

MatrixRank of a large but sparse matrix

I want to find the rank of a very sparse, quite rectangular matrix mat, but I'm running out of RAM (I have 16 GB) if I try to use ...