Questions on the manipulation of matrices in Mathematica.

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0
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0answers
46 views

Difference between matrix rapresentation [duplicate]

I've noticed different behaviour in Mathematica between matrix representation: The matrix a={{1,2},{3,4}} is different from b=a // MatrixForm Why i obtain ...
0
votes
1answer
192 views

Pattern match with Table for matrix dimension check

In Mathematica, often an expression involving matrices will encounter dimension mismatch errors, like we are multiplying a 3x2 matrix to a 3x4 matrix. Below we define a new symbol Dim, which can be ...
3
votes
2answers
375 views

Optimizing functions taking matrix arguments

I'm looking for general information on how to optimize matrix valued functions, I have the following function I'm looking to maximize (or figure out if this is possible at all). ...
1
vote
2answers
583 views

extracting the rows of a matrix satisfying a condition (e.g. all elements negative)

I have a matrix with thousands of rows and want the submatrix comprising the rows of the original matrix that have, e.g. a negative element in column 3. How to do that?
3
votes
2answers
410 views

Expanding Matrix Expressions

I want Mathematica to recognize that A.(-B.C)+A.B.C = 0 Yet FullSimplify and the like leaves the expression as it is. How do I get around this?
0
votes
1answer
638 views

Add a sub-matrix of zeros in big matrix [duplicate]

I have a matrix of size $24\times24$ composed by 8 $3\times3$ submatrices in a diagonal way. I want to add a matrices of zeros ($3\times3$) between the sub-matrices, so the final matrix would be of ...
2
votes
3answers
2k views

Saddle Point in Matrix

Here is the Problem how to find out the Saddle Point inside Matrix. m = {{9, 3, 1, 8, 0}, {6, 5, 4, 6, 7}, {2, 4, 4, 3, 8}, {5, 6, 2, 2, 1}}
2
votes
1answer
433 views
2
votes
2answers
445 views

Mass Symbolic Manipulation with Subscripts? (from plaintext Input)

The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν: expr = 3nu*kx*ky+ ...
1
vote
1answer
218 views
3
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1answer
125 views

Optimizing a simple calculus using a list of matrices - Repeated dot product between a vector and a list of matrices [closed]

I want to make the following operation : $$ \begin{bmatrix} \dot q_1\\\dot q_2 \end{bmatrix} + \begin{bmatrix} \begin{bmatrix} q_1 & q_2 \end{bmatrix} \mathbf A_1 \begin{bmatrix} q_1\\ q_2 ...
3
votes
1answer
125 views

How do I access the binary matrix underlying an EdgeDetect output?

Applying EdgeDetect to an image generates a black and white edge-detected image, which I suspect corresponds to an underlying binary matrix. How can I access this ...
1
vote
1answer
246 views

Why is arithmetic faster for inexact arithmetic?

I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...
0
votes
2answers
167 views

Import matrices side-by-side separated by TAB

The problem is 0(TAB)0 interpreted falsely as a dark red square although it should be a dark red square surrounded by zeroes/ones. Import has different data-formats ...
5
votes
6answers
936 views

A matrix-vector cross product

I want to do a cross product involving a vector of Pauli matrices $\vec \sigma = \left( {{\sigma _1},{\sigma _2},{\sigma _3}} \right)$; for example, $\vec \sigma \times \left( {1,2,3} \right)$. ...
1
vote
1answer
400 views

How to normalize parts of matrix elements?

To normalize the last 2 or more columns of a matrix, ...
0
votes
0answers
455 views

Solve equations real and imaginary part separately

For my system of equations, the procedure described in Solving complex equations of using Reduce works no more. How can I separate the real and imaginary part of ...
3
votes
1answer
223 views

How do I plot Numerical Range of two hermitian matrices

Let $A_1$ and $A_2$ be two $3\times 3$ hermitian matrices. Then their numerical range is defined as two-dimensional set \begin{align} \mathbb{S}=\{\left[u^HA_1u,u^HA_2u\right]\in ...
3
votes
1answer
192 views

Exploiting self-adjointness when changing basis

I am using Mathematica to analyze a real, self-adjoint matrix $H$ of the size $32 \times 32$, which comes from a physics problem. In the picture there is also a matrix $Q$ which commutes with $H$. I ...
5
votes
0answers
525 views

Export matrix to $\LaTeX$ with style

Is it possible to export a matrix to $\LaTeX$ with style? For example this code will create a matrix with equal spacing matrix and with background colors in some cell, is it possible to export that ...
3
votes
2answers
271 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 ...
3
votes
1answer
134 views

Defining an Implies operation that works for Boolean matrices

I have two Boolean matrices, that both have dimensions m x n. I want to create a function TableImplies, which would return True ...
8
votes
3answers
274 views

Declaration of abstract matrices to perform series expansion on them

I would like to have abstract matrices M and S to get out the coefficients of matrix power series however it treats M and S as numbers even if i checked that M.S - S.M != 0. I attach my code below: ...
3
votes
3answers
280 views

Matrix multiplication that includes a tensor

How would I best express the following in Mathematica: $\begin{pmatrix}2 & 4\end{pmatrix} \begin{pmatrix}r_1 & r_2\\r_3 & r_4\end{pmatrix} \begin{pmatrix}6 \\ 8\end{pmatrix}$, where $r_i$ ...
1
vote
1answer
274 views

Partial row reduction of a matrix

I have an $m\times n$ matrix (presumably of full rank) with $m>n$, and I would like to row reduce it, but leave the last column unreduced; that is, I want to get output on the form $\pmatrix{ 1 ...
5
votes
4answers
1k views

How to find the index of a square matrix in Mathematica quickly?

Let $A$ be an $n\times n$ complex matrix. The smallest nonnegative integer $k$ such that $\mathrm{rank}(A^{k+1})=\mathrm{rank}(A^{k})$, is the index fo $A$ and denoted by $\mathrm{Ind}(A)$. I would ...
1
vote
2answers
1k views

large matrix eigenvalue problem

I need solve a very large complex matrix (not sparse and not symmetry) eigenvalue problem, e.g., 1e4*1e4 or even 1e6*1e6. How large dimensions of the matrix can Mathematica support? And, how about ...
2
votes
0answers
195 views

Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)

I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
5
votes
3answers
847 views

Compute the rank of a matrix with variable entries

Say I have a matrix like $$ M=\left( \begin{array}{c c c} x & xz & w-2x \\ wz^3 & xy & z \\ y^2-z^3 & x+w & z+x^5 \end{array} \right) $$ is it possible to ask Mathematica ...
1
vote
2answers
665 views

Matrix echelon/upper diagonal form

Is there a way to find the echelon form of a matrix in Mathematica? I see there is a function to find the reduced echelon form, RowReduce[], but I can't see ...
0
votes
0answers
255 views

Defining and Solving Systems of Equations Using Matrix Tables

I've defined a system of equations, but I been unable to get Mathematica to solve for the individual variables created by matrix tables. ...
2
votes
3answers
403 views

Dynamically filling matrix with a[[n,m]] = 1/a[[m,n]]

I'm building a square matrix, with 1s on the diagonal and elements in U the inverse of elements in L, which are random integers drawn from the sequence 1, ..., 9. Given the nature of the problem I ...
2
votes
2answers
133 views

changing a symbol into a function variable

Struggled for a while on this problem and hopefully you can help... I have a mathematical expression that currently has a symbol where I used to have a function variable. How do I make the symbol ...
1
vote
2answers
253 views

Computing distance matrix for a list

Using functional programming in Mathematica, how can I compute a distance matrix for every element in a list of matrices... The distance would be computed between the item in the list and a "target ...
9
votes
5answers
587 views

Is there a built in function to obtain the back diagonal of a matrix?

Given the following matrix: m = Array[Subscript[a, #, #2] &, {4, 4}] how can I find the skew diagonal or anti-diagonal or back diagonal of the matrix ...
1
vote
1answer
246 views

Weighted Kirchhoff Matrix?

I have a weighted graph and I want its graph Laplacian matrix (what Mathematica calls the Kirchhoff matrix in the unweighted case). Is there an easy way to get this? For example, the command: ...
4
votes
2answers
1k views

Efficient ways to create matrices and solve matrix equations

I am attempting, for the first time, to use Mathematica to do some serious linear algebra. I would like to solve systems of equations of the form $$U_{n n'} f_{n'} = b_n.$$ I have an expression for ...
0
votes
0answers
37 views

Symbolic Calculations with formal matrices [duplicate]

I want to make calculations with matrices in the form (for lovers of statistical mechanics, is just the first step replica symmetry breaking) ...
15
votes
6answers
703 views

Matrix Rotation

If I have a matrix of any size, say $\begin{pmatrix} 72 & 32 & 64 \\ 18 & 8 & 16 \\ 63 & 28 & 56 \\ \end{pmatrix}$ $\begin{pmatrix} 72 & 32 \\ 18 & 8 \\ 63 ...
8
votes
1answer
196 views

Is it possible to lower the bitwidth of (floating point) numbers?

The answer to this question will most probably be a definite no. Nevertheless, I would like to know whether it is possible to represent reals in the memory on less than the standard 32 or 64 bits ...
-1
votes
2answers
753 views

Convenient methods to sum select rows (or cols) of a matrix? [duplicate]

What are some convenient methods to sum selected rows or columns in a matrix? This question Summing along rows or columns of a matrix only addresses how to sun entire rows or columns ie, by level. ...
4
votes
1answer
158 views

Using the mouse coordinates to index a matrix

I would like to "write" on to a matrix using the mouse. That is, I would like to use the integer value of Locator coordinates (p) to index a matrix. Then, if the mouse button is down, write a 1 in ...
1
vote
3answers
142 views

Define new number set

May seem strange at first, but can you make mathematica change the value of 0 to 10 and 11 to 1 for all occurrences. Let me explain: I'm looping through a matrix and for each element, I want ...
-5
votes
5answers
555 views

Translating MATLAB's cell2mat into Mathematica

How I can define a function in Mathematica such that it acts same as the cell2mat command in MATLAB? Example (in MATLAB): ...
1
vote
2answers
799 views

How do I divide the columns of a matrix by the sum of its elements?

I am trying to create a transition matrix for a network. In order to do this, I need to sum down the column (the out degree), and then divide the column by the out degree in order to normalize it. ...
0
votes
3answers
308 views

Matrix Determinant

I have an N by N (N>3) matrix generated from fortran. I would like to find determinant of that matrix using mathematica? I could do this for a 3 by 3 matrix. I can also import the fortran output file ...
4
votes
2answers
263 views

Sorting a matrix alphanumerically

Somewhat related to Sort matrix by columns and rows without changing them, but more general. I'd like to sort a square matrix (a 3 by 3 in my case, but surely the general solution will treat any), ...
-2
votes
1answer
216 views

Fortran kind of matrix creation [closed]

I want to create the matrix H of dimensions nxn and matrix elements H(i,j). Because of the physical problem I am dealing with, it is necessary to build it in the following not trivial way. I know how ...
0
votes
1answer
162 views

Get value only from Position

If have the following command Position[{a, b, a, a, b, c, b}, b] (* Out[1]= {{2}, {5}, {7}} *) Is it possible to get only a sequence of values instead of this ...
2
votes
3answers
559 views

Convert coefficients of polynomials into a matrix

I have several sets of 5 polynomials of the form: ...