Questions on the manipulation of matrices in Mathematica.

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11
votes
1answer
149 views

Why FoldList 5 times faster than Apply for matrix multiplication? [duplicate]

Consider this list of $2\times 2$ matrices: list=RandomReal[{-2,2},{500,2,2}]; Now compare timings of Apply and ...
3
votes
1answer
116 views

Optimize a parametric matrix to get a lowest possible eigenvalue

This question is a followup of Plot the lowest eigenvalues of a parametric matrix Now I can get the lowest eigenvalue LowEign(t) of the matrix for a given t numerically. When I plot the LowEign ...
0
votes
2answers
63 views

Automatic process to replace missing values, coming from a second matrix

I have a large starting matrix with missing values in different columns. I want to replace this missing data as follow. First I have to check the group (last column in starting matrix) and go to a ...
2
votes
1answer
61 views

Plot the lowest eigenvalues of a parametric matrix

The question here is somewhat related to the comments in Computing eigenvectors and eigenvalues I have a matrix M, say 400 by 400, and all elements depend explicitly on one parameter t in a ...
26
votes
2answers
6k views

How to form a block-diagonal Matrix from a list of matrices?

For example, like this: I know join[...] works, but it is a bit troublesome for multiple matrices. I also tried DiagonalMatrix[...], but DiagonalMatrix can only form a matrix from a list of ...
0
votes
3answers
84 views

How do I create a circulant matrix? [closed]

How do I create an $n \times n$ circulant matrix? I couldn't make ToeplitzMatrix do it for me.
1
vote
1answer
25 views

Passive Transformation does not return the expectedt result due to precision of expressions

So I wish to perform a passive rotation in N dimensional space. Let me take N=5 for this question. ...
1
vote
1answer
108 views

Evaluate pure function through round brackets

In have some matrices of pure functions or numbers which I multiply by other matrices or vectors. I would like the functions to be evaluated in the result, but all that I get is something like this: ...
1
vote
1answer
71 views

Create a Dataset object, Association or SparesArray from a matrix [closed]

I need to make queries and operations on a large dataset. What is the easiest way to add keys to matrix so that it is transformed to a dataset, which can later be used to make queries? Let's take ...
2
votes
2answers
110 views

Delete rows and columns in a matrix based on the element index

This is a follow-up question from here: Define a 4d matrix without for loop I have a 400x400 2d matrix reshaped from a 4d matrix H(i,j,k,l), ...
2
votes
2answers
87 views

Define a 4d matrix without for loop

I was wondering if there is a way to avoid for loop here: I want to define a 4d matrix H(i,j,k,l), and each entry in the matrix is calculated through a complex function, say Do_H(i,j,k,l), depending ...
1
vote
2answers
99 views

Find the minimum element of a row of a matrix and its column index for each row

I am trying to find the minimum value of a row of a matrix and its corresponding column. Please run the code below. OptV is the matrix that I would like to create which must give the output of the ...
6
votes
2answers
125 views

Good way to create a similarity / distance matrix for a large dataset [duplicate]

I have a large dataset with rows (100k+) for products and columns for features. Now I want to create a similarity matrix with NormalizedSquaredEuclideanDistance. ...
0
votes
0answers
45 views

Value Iteration (Recursive iteration) to Minimize (Optimize) a Function

I have a function that I call as "Value". I am trying to find the minimum of this function and this function is a function of 4 other functions. One of these four functions is recursive based on the ...
1
vote
1answer
150 views

How do you solve a linear equation of matrices? [duplicate]

The function Solve works fine for scalars: In[]:= Solve[A x - x B + C == 0, x] Out[]= {{x -> -(C/(A - B))}} When using matrices however, ...
2
votes
1answer
39 views

Square bracketed matrices in Mathematica - precision markers?

I'm trying to display Matrices with square brackets in Mathematica. I've found this post from a mailing list in 2009 http://forums.wolfram.com/mathgroup/archive/2009/Aug/msg00458.html and it seems to ...
6
votes
1answer
131 views

Calculate the ESP Grid based on Density Grid

I want to build a fast way to convert a density grid file into a grid file of the respective electrostatic potential (ESP; also known as MEP, the molecular electrostatic potential). This ...
5
votes
4answers
449 views

How to simplify block of multiple repetitive If statements?

I'm building a boardgame...game in Mathematica. I have the board state represented as a matrix. It's a two player game, and each player (let's call them A & B) only has one type of piece or ...
0
votes
2answers
91 views

I'm trying to solve a system of complex equations

I'm simply trying to solve a system of equations and mathematica can't do it for all values over the region of interest. I have a 3x3 matrix that has a specific parametrization and after squaring the ...
1
vote
2answers
91 views

Plot values of an $m\times n$ matrix on the complex plane with color varying along $m$

Let's say I have a complex valued matrix $\begin{pmatrix}1+I&2+2I&3+3I\\4+4I&5+5I&6+6I\end{pmatrix}$ represented by a list: ...
11
votes
9answers
743 views

Forming an upper triangular matrix from the elements of a list

I asked this question before, but i was closed because it the question was not comprehensible enough. So i reworded it, hope that's ok. I have a list with 6 elements. ...
1
vote
0answers
43 views

Generating random Kraus operators

I am trying to generate (randomly) set of square matrices $\{K_m\}$ with the properties that $$\sum_{i=1}K_i^{\dagger}.K_i=I_n,$$ where $I_n$ is the identity matrix of order $n$. So, the input should ...
0
votes
1answer
30 views

Iterating KroneckerProduct[] and returning the result from a function

I am trying to write a function which will take a matrix m and an integer i as inputs. Then it will compute the Kronecker product of m with itself i times and return the result. The code is as ...
2
votes
1answer
62 views

Accuracy limitations of singular value decomposition?

in the process of working on a physics problem I have found the need to use the singular value decomposition function built into Mathematica. I have encountered what seem to be limitations to the ...
1
vote
0answers
50 views

Dealing with answers that have Root[ …] when finding an Eigensystem [duplicate]

This is a 3x3 matrix and I think it should solve for the expressions in terms of radicals. I am not sure what to do with this.
1
vote
0answers
146 views

Request for clarification of Eigensystem::eivn message

What causes the problem of "two eigenvectors associated to one single multiplicity eigenvalue" that I am experiencing? After several transformations to simplify an unwieldy matrix, I end up with the ...
0
votes
0answers
95 views

Is Eigensystem::eivin message a bug?

I noticed that in the question Request for clarification of Eigensystem::eivn message the error message Eigensystem::eivn: Incorrect number 2 of eigenvectors for eigenvalue ...
0
votes
1answer
88 views

How to get rid of # in answer (eigensystem)? [duplicate]

I was trying to find the eigensystem of the following matrix (act as if the second character is in subscript): \begin{pmatrix} 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ ...
6
votes
4answers
3k views

I need to multiply a series of matrices

I need to perform a dot product on a large number of 2 x 2 matrices that I have defined to differ by even/odd subscripts (Ex: D-odd=x but D-even=y). The $\Pi$ function will not work because it does ...
0
votes
0answers
29 views

factoring a phrase of matrix elements and calculating main eigenvalues

I have a question containg two parts: 1-If we have a matrix as ...
0
votes
1answer
48 views

Inverse of a Fourier matrix [closed]

I am trying to find the inverse of a Fourier matrix but I am getting confusing results. If R is a Fourier matrix, then ...
6
votes
3answers
312 views

Indicate minimal path sum

Described on the page: http://www.mathblog.dk/project-euler-81-find-the-minimal-path-sum-from-the-top-left-to-the-bottom-right-by-moving-right-and-down/ It is an example of the solution indicated in ...
0
votes
1answer
48 views

How to pad numbers to the border of the Matrix?

I want to pad the numbers,but it throws an error Part::partw,so I use Quiet to suppress this error. ...
0
votes
4answers
50 views

insert elements into 2 D array [duplicate]

say I have a 2 dimensionsal array like a={{1,2,3},{4,5,6},{7,8,9}} and a vector like v={10,11,12} I want the result to be ...
1
vote
0answers
47 views

Working with matrix

Considering the 3x3 matrix: m = {{0, -(I/Sqrt[2]), 0}, {I/Sqrt[2], 0, -(I/Sqrt[2])}, {0, I/Sqrt[2], 0}} How would I find its normalized vectors eigenvectors u_i ...
3
votes
0answers
66 views

Why does Eigenvalues work for a matrix $\{M\}$ but not $\{\{M\}\}$?

Suppose I have a matrix {{1, 2}, {3, 4}} which I'll call mat. In a blur of human error, I computed the eigenvalues of ...
0
votes
1answer
91 views

How to turn a subroutine into a function?

I've written a subroutine that takes in 6 matrices and after some manipulation returns back 3 new ones. I will use this subroutine fairly often in this notebook so I think it would be easier to turn ...
-1
votes
1answer
64 views

Real and Imaginary matrix

I have a 2 by 2 matrix T: {{x, y}, {-y, x}} where x is the real part of some complex number and y is the imaginary part of something complex number. Let's say z1 = ...
1
vote
0answers
37 views

Getting the row/column reduction matrix of a matrix m

Is there a simple way to get the row reduction matrix for a matrix m? As in, a matrix a such that ...
2
votes
0answers
67 views

Unexpected behavior from applying ToRadicals to eigenvalues [closed]

I am trying to get the symbolic form of a $10 \times 10$ matrix (I know, that is generally too large). ...
5
votes
3answers
242 views

Assumptions for RotationMatrix

I'm making C++ program, and in my program I need a rotation matrix around any vector. I wanted to extract RotationMatrix[fi,{x,y,z}] output and put it in my ...
3
votes
0answers
78 views

Real Canonical Form of Arbitrary Size Matrices

I have been searching the site and the Mathematica documentation, but have not found anything regarding this. If we find the Jordan Form of the following matrix, we get complex values, but I would ...
1
vote
0answers
78 views

Outer product using the quantum mathematica package

I am using the quantum Mathematica package and am trying to do computations that require me to use the outer (tensor) products of Pauli matrices. I would define this as, for example, ...
1
vote
2answers
62 views

Trouble implementing logarithmic matrix norm

I wanted to write a quick function that calculates the logarithmic matrix norm with respect to the spectral norm. The formula is $$ \mu_2(A) = \lambda_\mathrm{max}\left(\frac{A + A^T}2\right). $$ So ...
2
votes
0answers
45 views

Optimization for iterating and plotting a matrix product and its elements?

I have an iterative matrix product of this type Since i didnt knew how to do it, I explicitly wrote the product as {Ayn + Bxn, Cyn + Dxn} and evaluated it with the NestList construct ...
11
votes
4answers
484 views

How do I extract a matrix of only positive numbers given a set of assumptions?

I want to divide a matrix: mat = {{a, 0, -b}, {d, a, 0}, {0, 0, -a}} with the following assumptions: ...
0
votes
1answer
49 views

Overriding Subscript operator creates its own variables?

I tried to override the Subscript operator to make matrix indexing a bit more "user-friendly" in complex expressions with the following code according to the ...
5
votes
1answer
80 views

GaussianMatrix function issue

Here is my implementation of the built-in GaussianMatrix function. ...
10
votes
10answers
682 views

Matrix indexed by one number

I'm trying to find a generic way (for arbitrary dimensions) to create a matrix like so a[1] a[2] a[3] a[4] i.e where it is indexed by one number, instead of say ...
3
votes
2answers
87 views

Perform matrix/tensor contractions more efficiently

Problem: explicit index contractions for matrices using the Sum command take too long, and I want to improve the performance for complicated computations. Let me ...