Questions on the manipulation of matrices in Mathematica.

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2
votes
1answer
132 views

How to swap tensor indices without permutation?

Say I have a tensor of rank R, How to swap $i^{th}$ and $j^{th}$ tensor index? I do not want to use TensorTranspose because it requires to write down the entire permutation, i.e. ...
4
votes
1answer
181 views

Proving positive definiteness or semi-definiteness of a matrix

I have the following 4x4 real symmetric matrix: $K=\begin{bmatrix}3-3w & -\frac{4}{3}+a+2w & \frac{5}{12}+b-\frac{w}{2} & 0\\ -\frac{4}{3}+a+2w & -1-6a-3x & ...
4
votes
1answer
533 views

Principal Components - how to obtain linear transformations?

I have a list "xlsf" with 6 columns and 1200 rows for PCA analysis. The PrincipalComponents[xlsf] gives the following: "The principal components of matrix are ...
3
votes
1answer
281 views

Spectral Clustering

I am attempting to implement a spectral clustering routine using Mathematica, but I am encountering difficulties. Using the standard Gaussian similarity function found in section 2.2 of this paper ...
8
votes
3answers
538 views

Plotting triple data points while xy data are not regular

I plotted recently some figures in Matlab and their quality was not that satisfactory, so I come to Mathematica as my supervisor suggested. This is how such figure looks like in Matlab: . In Matlab, ...
10
votes
1answer
336 views

Drop selection of columns from a ragged array

I have an application where I need to drop some arbitrary list of columns from a ragged array (where of course the shortest array rows have at least all the specified columns). E.g., given a ragged ...
8
votes
2answers
651 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
4
votes
2answers
208 views

Improve simulation speed using Compile

I have two square matrices, a hermitian matrix h and an unitary matrix v. I am interested in the following function ...
0
votes
1answer
100 views

Creating Matrix,Inverted and Upper Triangulate inside Module

I was trying to fit this into a module but I didn't have any luck. And for some reason it won't Inverse the Matrix. Here's the code: Input: ...
107
votes
7answers
34k views

Elegant operations on matrix rows and columns

Question The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a ...
-1
votes
1answer
69 views

Help needed with assignment [closed]

Can I get some help with this: Write a module which as an input receives two matrices, the first matrix transforms in to the same matrix, but in the new matrix occur absolute values of the first, ...
6
votes
2answers
961 views

Sort matrix by columns and rows without changing them

I would like to sort a matrix in descending order first by the total of each column, then by the total of each row, but without changing their content. For example, if I had: ...
0
votes
0answers
68 views

Which method to use for finding maximum without actually computing optimization function explicitly?

I am new to Mathematica and I am currently working on an optimization problem. The optimization function that I have easy to calculate for some assignment of variable but it is very difficult to ...
-1
votes
1answer
103 views

Module whose input is a function of 2 variables [closed]

I need to make a Module whose input is a function of 2 variables and 2 variables m,n so i can make a Matrix with Array. Basicaly, I need this: ...
1
vote
2answers
96 views

Matrix with infinity on main diagonal

The question is trivial, however, there might be unexpected solutions. What would be nice way to create a square matrix with $\infty$ on main diagonal, and some arbitrary constant everywhere else? My ...
3
votes
2answers
440 views

How to make Mathematica show matrices and vectors nicely

It shows me like {{0}, {1}, {0}, {-1}} . Is it possible to make it look like a vector, always?
3
votes
2answers
295 views

Binarizing a matrix

I have an image with a few bright pixels with the remaining ones very dark. The difference is in orders of magnitude. I want to binarize this matrix (corresponding to the image) making all values ...
0
votes
0answers
68 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
126 views

Extract coefficient matrix $A$ from expression $f(x)$

I have expression: $$f(x)=\sum_{i=0}^{K-1}\sum_{j=0}^{N-1}a_{i,j}e^{ix}x^j.$$ I want to extract coefficient matrix $A$ from expression $f(x)$ where $$A=\left( \begin{array}{ccccc} a_{0,0}& ...
0
votes
1answer
80 views

Symbolically solve system of equations involving matrix

I need to solve the following system of equations symbolically for a_i, b_i, and c_i: ...
8
votes
3answers
1k views

How to manipulate gauge theory in Mathematica?

I want to know if there is a way of typing into Mathematica an expression like the following, $$\epsilon^{\mu \nu \lambda} f^{abc} A^a_\mu A^b_\nu A^c_\lambda + g\epsilon^{\mu \nu \lambda} A^a_\mu ...
2
votes
0answers
209 views

Factor out a constant from a matrix [closed]

I've got a matrix in which every entry is of the form x/4. I cant find out how to factor out the 1/4 so that the actual matrix is clearer. Thanks for your help!
3
votes
1answer
73 views

Efficient Implementation of Resistance Distance for graphs?

Is there an implementation of the resistance distance matrix (or just resistance matrix) for graphs available in Mathematica?
0
votes
0answers
45 views

in the part assignment is not a symbol, create different matrices with a “Do” loop [duplicate]

Im trying to assemble new matrices from some previous matrices I have created, but I can´t. What Im trying to do is the following: 1) I have different matrices: ...
0
votes
1answer
55 views

Returning functions that are partly evaluated

I have some performance issues when calling Table[{h, Slow1[h, n]}, {n, nlist}, {h, 0.1, 10, 0.5}]; for a given list ...
2
votes
1answer
129 views

How to construct a kernel from a function?

I would like to convolve an image with a mathematical function. I understand that I need to have the mathematical function in a matrix form. How can I build it? Thanks
12
votes
1answer
296 views

Why does partitioning increase Dot execution speed?

I have noticed that multiplying a list of matrices can be significantly sped up by partitioning the list, calculating the product of the partitions matrices, and then multiplying the results. ...
2
votes
1answer
346 views

Usage of Piecewise/RSolve to solve an equation based on condition

I am trying to compute price of call option on a stock using the finite difference method. I have a VBA code for it, and I am trying to find out how I can use Mathematica memoization functions and ...
0
votes
1answer
174 views

Symbolic matrix inversion

If I try to get an inverse of a matrix: a | b | c b | d | 0 c | 0 | 0 Inverse[{{a, b, c}, {b, d, 0}, {c, 0, 0}}] I get the answer: ...
0
votes
3answers
63 views

Simplifying Terms in a Matrix

Given the following 3 matrices: M1=1/3*{{1,1,1},{1,α,α^2},{1,α^2,α]}} Z1={{Z+Zg,Zg,Zg},{Zg,Z+Zg,Zg},{Zg,Zg,Z+Zg}} M2={{1,1,1},{1,α^2,α},{1,α,α^2}} where alpha ...
0
votes
2answers
41 views
-1
votes
1answer
87 views

Beginner Question: Assigning an indexed Variable to a given list

I am pretty new to the game and have a problem, which i am sitting on for hours. 1) I created a random Matrix 5x5 ...
1
vote
1answer
165 views

Divide each element of a list of 500 matrices by another matrix

Lets say that I have a Table of dimension (3,3,500) and I'd like to perform element-wise division by a 3x3 matrix along the third dimension (of length 500 in this case). What is the most elegant way ...
9
votes
3answers
1k views

The magic square function

There're some matrices that the sum of columns, sum of rows, and sum of diagonals are the same value. Here is an example: ...
1
vote
1answer
79 views

Assigning some results after a solve procedure to the coefficients of a matrix

I have a matrix M[3,3]. After a solve procedure, I obtained these results. {{M[1, 2] -> Cos[ψ[t]], M[1, 3] -> 0, M[2, 3] -> 0, Cos[θ[t]] -> M[3, 1], M[3, 2] -> 0, M[3, 3] -> 1, M[2, 1] -> ...
0
votes
0answers
46 views

Parametrizing a matrix given its trace and norm

I have a problem where I have to generate random matrices with the following properties: ($a$ is a given fixed number) $\mathrm{Tr}\, A=0$ $\mathrm{Tr}(A^\dagger A)=\|A\|_F^2=a$ I was wondering ...
4
votes
4answers
152 views

Express block matrix in terms of matrix basis

I'm trying to construct a function that returns the multiplication table of a matrix Lie algebra. Assuming a basis of matrices, my definitions: ...
-1
votes
1answer
109 views

Laplace equation

I tried to run this code, but it doesn't work for NDSolve ...
5
votes
4answers
203 views
2
votes
1answer
139 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 ...
4
votes
2answers
154 views

Gridding in a Nested Matrix

We have a nested matrix as: nested={{he, {{e, f, g, h}, {s, 0, q, i}, {s, 0, q, j}}}, {ho, {{e, f, g, h}, {0, u, t, i}, {u, t, 0, j}}}} and with the line ...
4
votes
4answers
778 views

Writing a circular matrix

I have two square matrices, $A$ and $B$, of the same size, say, of $m \times m$. What I want is to write a programme/function of three variables, $A$, $B$ and $n$, that outputs the $mn \times mn$ ...
0
votes
0answers
69 views

Deciphering output messages using Solve

I'm trying to solve the following system. The error messages I'm getting suggest that there may not be a solution [my desired result], but I'm not sure if there could be something else going on. The ...
1
vote
3answers
147 views

Absolute VectorPlot scaling

I'm trying to visualize the vector components of a rotation matrix with absolute vector lengths. VectorScale help states that When using an explicit sfun, ...
1
vote
1answer
104 views

Getting a part of a matrix Inverse for later use

I was trying to get an element of a matrix, and use in further computation of my program. Problem was that its not reading the value unless and until I specify it again. My code is: ...
3
votes
2answers
283 views

How to rewrite this function to be faster: Find sub-matrixes of boolean board which imply a given boolean pattern

I have Boolean matrix A (called "board") and Boolean matrix B with smaller dimensions (called "pattern"). I am trying to find sub-matrixes C of A such that C has same dimensions as B, and ...
0
votes
0answers
71 views

Matrix iteration failing after second step

I am calculating 11x6 matrix using different logics as in below code. Problem is in Do loop in below code where I have two different criteria to update matrix "fd". I am expecting logic in IF which ...
0
votes
1answer
61 views

Replace element of matrix based on rule which invloves other element of same matrix

I am trying to replace 1s row of matrix d iteratively from right by multiplying last element in 1st row with (1-int*dt) to generate 2nd last element. The replacement continues till I reach the 1st ...
2
votes
1answer
84 views

Abstract iterator in Do

I'm trying to write a module. Its input is a matrix (tensor), the module should return new tensor with increased rank with 1. The new tensor is defined as $$ O \Rightarrow N_{\alpha \beta \ldots ...
1
vote
2answers
94 views

Problem in matrix multiplication

I created a random directed acyclic graph using Mathematica. I need to compute a specific function from its adjacency matrix. ...