Questions on the manipulation of matrices in Mathematica.

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1
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2answers
95 views

Group matrix values by column [closed]

Original Question: I have a list {{a, 1}, {b, 3}, {c, 1}, {d, 2}, {e, 3}}. I want to be able to group the the first number in each pair that has the same second ...
3
votes
1answer
102 views

Efficiently compute this Table of NullSpace

I have two $(2n,2n)$ matrices, $A_1$ and $A_2$, and I would like to compute $$\ker(A_1^p A_2^q -I)$$ for $p,q\leq 2n$. Both matrices are orthogonal and have exactly four non-zeros values on each ...
2
votes
5answers
194 views

Finding the most common n-tuples of a list of lists where order does not matter

I am still learning to use Mathematica and I need some help. How could I get the most common pair, and generally the most common n-tuple of a list (row vector) given a list of lists of ...
1
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2answers
228 views

MatrixPower performs slower than Do loop

I have two almost identical pieces of code: one with MatrixPower responsible for matrix multiplication and another with Do loop. Why the latter performs much faster? It looks counterintuitive... <...
2
votes
1answer
155 views

How to sort eigenvalues?

I am trying to find Eigenvalues to a 12x12 Matrix ($H$) dependent on two variables $x$ and $y$. Later I want to do a 3D plot of one eigenvalue ($E$) over $x$ and $y$. An analytical solution is not ...
1
vote
1answer
83 views

Matrix equations solving

can you explain me the easiest way for solving this matrix equation? I have this matrix: a={{-4,1,3,0},{-2,7,1,-1},{1,-1,9,-3},{-1,0,5,-10} and the Equation is: ...
0
votes
1answer
55 views

How to generate a random matrix and its average value is a specified value

I want to generate a random matrix whose average value is a specified value,such as 5.5. I found these function here.But I don't know how to use it to do this.I think ...
0
votes
1answer
67 views

How to map data from one set to another set

I have a set of numbers that has a non-injective, surjective correspondence to another set of numbers and I would like to quickly create a list of the output. For example, suppose I have ...
2
votes
0answers
28 views

Using Arnoldi Method with Multiple Options

I have a matrix with many complex eigenvalues, but I only need a few near a particular complex number. I am only looking at the imaginary parts, so I need the few closest on the imaginary scale to my ...
-1
votes
2answers
58 views

Rearranging the columns of a matrix [duplicate]

How do I rearrange the columns of a matrix? I really have o idea how to do this. Thankfs for any suggestions!
3
votes
1answer
49 views

Use of Inverse Matrix

I solved a matrix as follows: {{0,1,1},{0,2,4},{0,3,9}}.{{0},{25},{20}} Resulting: {{45},{130},{255}} I tried to use an ...
8
votes
2answers
307 views

Why is IdentityMatrix not defined as a SparseArray by default?

Simple (possibly silly) question: why are IdentityMatrix, DiagonalMatrix, ConstantArray ...
1
vote
1answer
44 views

Solve matrix equation for matrix

Is there any function like Solve but designed to deal with matrix equations? Something like: ...
3
votes
1answer
107 views

Irreducible representations for the symmetry group $T_d$

I am trying to get the explicit two dimensional irreducible representation matrices for the symmetry group $T_d$. I need the matrix representation for each element in the group. Are there any ...
1
vote
1answer
69 views

generating random algebraic matrix using elementary operations

I generate several algebraic matrices of 12x12 where each element is a combination no repeat of the variables x, y, z and operations +, -, *, /, power, establishment (square root), any of them or any ...
3
votes
2answers
79 views

Creating a constant-valued matrix having the same dimensions as previously defined matrix

I have the dimensions of a matrix A. I would like to create a matrix B (say, of only 0's) of the same size as A. But A's dimensions are variable. Is there an efficient way using ...
0
votes
1answer
51 views

How can we do LDU decomposition modulo $p$?

If we have an $n \times n$ matrix, with all entries taken modulo $p$, how can we output the three matrixes in LDU decomposition, with all entries again modulo $p$? We can assume the input matrix is ...
3
votes
1answer
75 views

Implementing the Cimmino method [closed]

What am I doing wrong? I am trying to implement the Cimmino method, an iterative method for the solution of linear algebraic systems. The final output should be a vector. Here is a description of the ...
-1
votes
1answer
61 views

How to solve trigonometric matrix

I need help for my problem according to matrix. Given a matrix, ...
3
votes
2answers
165 views

How to Convert a Matrix into an Association?

I have a matrix like this one: test = {{1, "a"}, {3, "b"}} and I want to convert it into an association like this ...
2
votes
1answer
71 views

Symbolic vector addition

I'm trying to figure out a nice way to add a mix of symbolic and explicit vectors/matrices without mathematica treating the symbolic vectors as scalars and promoting them to constant arrays. For ...
0
votes
1answer
50 views

Evaluate polinom with matrices [closed]

Let's say that I have the following polynom f = a+b+ab I want to evaluate this expression like this: ...
1
vote
0answers
36 views

extracting families with their representatives and number of repetition [closed]

There is a matrix: {{1,1,1},{1,2,1},{2,1,1},{-2,-1,-1},{1,1,-2},{1,-2,2},{2,1,-2},{1,-2,2},{-2,2,1},{1,2,2},{2,2,2}} How we can extract another matrix which ...
1
vote
2answers
54 views

Random distribution of some Lists on a distinct matrix

I have 3 functions as below ...
3
votes
1answer
53 views

Constructing tensors with arbitrary rank and dimension [closed]

How can I create a tensor with arbitrary rank n and m components in each dimension? I am looking for a command in which I insert n and m and it spits out the corresponding tensor with random entries (...
3
votes
1answer
47 views

check content of a Matrix

I have a matrix which contain rotated ellipses and points, how can I check if the element in the position {i,j} is either a point or an ellipse? the code is a bit longer but the structure is like: ...
1
vote
1answer
71 views

Nonlinear Markov chain (numerical simulation)

Suppose you have a linear Markov process, and you can write it as x(t+1) = Ax(t). Here x is the vector of values, and A is the transition matrix. Since this is linear, it can be solved analytically, ...
-1
votes
1answer
68 views

How to correctly calculate symbolic eigenvectors

I give a minimalistic example of my problem: I have a matrix: m[a_,b_]:={{0,-a+b},{b,0}}; I define the eigenvectors as: ...
2
votes
1answer
80 views

Solving for five unknowns in a 3 x 3 matrix

I know that matrix.Transpose[matrix] = IdentityMatrix[3] matrix = {{0.8111, 0.4867, -0.3244}, {a,b,0}, {c,d,e}} I tried ...
1
vote
2answers
53 views

Plotting points using adjacency matrix

Given an adjacency matrix on n vertices and a polygon on n vertices, how to add edges from adjacency matrix on the Polygon? eg: if polygon is {(0,0),(0,1),(1,0),(1,1)} and the adjacency matrix has 1 ...
0
votes
1answer
44 views

Probems using 2 For and a AppendTo to cycle through my Equation to solve some matrixes

I am trying to solve a few problems here. I have an equation with multiple variables that I am trying to solve in For loop method. I will attach the file below. In addition I am trying to get it to ...
2
votes
1answer
52 views

Finding an Integer, Unimodular Matrix that connects two given matrices

I have two symmetric, integer matrices, $K$ and $K_2$ which have the same determinant and the same signature (number of positive - number of negative eigenvalues). I want to find an integer valued ...
1
vote
0answers
56 views

Map over multidimensional matrix [closed]

Suppose I have a 8by6by4by2by2 matrix called m. There is in total 8*6*4 2by2 matrices. I want to map a function over these 2by2 matrices. Each dimension in ...
5
votes
1answer
67 views

What's up with PauliMatrix with a string argument?

Looking at the definition of PauliMatrix (not the documentation), I realized that it is defined for arguments 0, ...
4
votes
1answer
155 views

Defining a matrix with elements acting as operators

This question is directly related with my previous one. I'll try to be more specific here. I have a matrix {{a[x],b},{c,d}}, where ...
0
votes
1answer
92 views

Accessing the elements in a table is slower than calculating each time?

This is a follow-up of How to accelerate combinations and sum calculations here? I have tried all tricks but when N reaches 35 the time is still intimidating in a 16-core server, which is far better ...
1
vote
1answer
93 views

Is it possible to decouple this Matrix A to matrix multiplication of two matrixs B and C?

I want to decouple this matrix A into two matrixs B and C, with A=B*C. And B is functions of r, C is functions of n. Is it possible or not? Can I use Mathematica to do this? Any help or advise is ...
0
votes
0answers
40 views

How to plot eigenvalues as a function of parameters in a dynamic module?

I am trying to make a fancy interactive plot that shows how the eigenvalues of a matrix mat change under variation of parameters ...
0
votes
1answer
69 views

Eigensystem with orthogonal elements in matrix

I have a matrix with 16 elements: matrix = {{f1, -f2, -f2, f3 }, {f4, -f1, -f1, f2}, {f4, -f1, -f1, f2}, {f5, -f4, -f4, f1}} I would like to calculate ...
6
votes
2answers
274 views

Find a condition that b must satisfy so that Ax=b has solution

I'm new to Mathematica, so I'm sorry if this is really simple. I am trying to find the condition that vector b must satisfy so that Ax=b has solution. I would like to learn a general method, but I'll ...
3
votes
4answers
121 views

mapping a smaller matrix in a greater matrix with a specific sequence

I have a matrix 300x300 i need to map the values ina greater matrix (900x900) in the positions given by the sequence $$({3*i-1,3*j-1)}$$ while everything else remain empty, how can achieve this ...
1
vote
3answers
92 views

How to Import and Export as a multidimensional array

I have 10000 matrices and each matrix is 3x3. So Dimensions[data] gives me {10000,3,3}. I saved this into a file with Export["mydata.dat",data,"Table"] Then when I imported it using Import["mydata.dat"...
1
vote
2answers
102 views

Output the tensor product of two matrix as a matrix

How do I output the matrix form like the RHS without the tensor product sign remaining $\otimes$? I need it for display purpose where I can see easily what the form of the whole product matrix is.
2
votes
1answer
64 views

How to accelerate combinations and sum calculations here?

I have a 4d matrix H defined as below (embedded with combinations and sums) ...
1
vote
1answer
60 views

Fast Eigensystem calculation

I have a code which finds the eigensystem for a matrix H = H0 + x HInt, where x is a variable which turns on the interaction. H0 is diagonal, and HInt is a sparse matrix (with about 400 states, I hope ...
0
votes
0answers
38 views

Matrix with equations as entries - how to choose them and solve them

I have a matrix in Mathematica, which I have built using Normal[SparseArray]. Each entry of this matrix is an equation in one variable. What I need to do is 1) to select some of the entries of the ...
3
votes
2answers
133 views

Replacing multiplication of matrix elements by application of these elements as functions

I want to realize the following idea in Mathematica. I've got a matrix {{a,b},{c,d}} which is multiplied to a vector {h,k} ...
2
votes
0answers
95 views

How does Mathematica compute the determinant of a matrix? [closed]

I have been trying to write efficient code for calculating the matrix determinant for some time now. I noticed last night that Mathematica is able to compute the determinant of a $200 \times 200$ ...
2
votes
2answers
98 views

Dynamically sized $n\times n$ checkboxes corresponding to a matrix

I was wondering if it was possible to do to following: have an input field for an integer where you input the $n$ have an $n\times n$ matrix of checkboxes that would correspond to an $n\times n$ ...
2
votes
1answer
70 views

Save a fraction matrix in Mathematica into C++ friendly format

In MMA I have a 2d matrix whose each entry is a irrational number(in fraction format in MMA). Say: ...