Questions tagged [matrix]

Questions on the manipulation of matrices in Mathematica.

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4
votes
1answer
435 views

How to create a SparseArray satisfying multiple conditions on Parts and Elements of a Matrix?

I have a matrix m1 of size $3 \times 19$. Rows $1$, $2$ and $3$ represent $3$ different groups, and columns represent $4$ different blocks: block1 - columns $1$, $...
4
votes
2answers
174 views

Permutations: selecting reviewers without conflicts of interest

I would like to automate the process of selecting a number of proposal reviewers that fit a conflict of interest criterion. Let's say I have 5 reviewers and 5 applicants from 5 departments. The ...
6
votes
5answers
1k views

What is the fastest way to replace all zeros in a matrix?

In the following matrix m every 0 should be replaced with a 1: m = {{0,1,2},{5,0,3},{8,0,0}} Desired result: ...
5
votes
2answers
656 views

Random Matrix with integer coefficients and inverse also having integer coefficients

I'm trying to build a function that gives me matrices such that each: Has integer coefficients. Is non singular. Has inverse which also has integer coefficients. I have some code that one of my ...
2
votes
1answer
2k views

Is LinearSolve the most robust way to solve the equation $Ax=b$?

I want to solve the equation $Ax=b$, where $A$ is an $n\times n$ matrix, and $x$ and $b$ are $n\times 1$ column vectors. Here $n=124$. LinearSolve[A,b] I got the ...
7
votes
2answers
2k views

Finding maximal sublist of linearly independent vectors

Given a list of vectors v = {v1, ..., vn}, which is the fastest way to find a maximal sublist of linearly independent vectors? I could add the vectors one by one to ...
3
votes
2answers
232 views

Write list of polynomials as a matrix of coefficients times a list of monomials

I have the following problem: given a list of polynomials P = {p1, ..., pn} on the variables x[1], ..., x[n], find a list of ...
0
votes
2answers
279 views

Deleting duplicates from matrix

I have a 4x4 symmetric matrix that is obtained by solving some equations. I tried deleting duplicates with DeleteDuplicates, but that's not working with nested ...
5
votes
2answers
402 views

Mixed product identity between tensors in Mathematica 9

How can we simplify tensor expressions in Mathematica 9 using the mixed-product identity $(A\otimes B)(C \otimes D) \equiv AC \otimes BD$ ? Is it possible to implement this kind of evaluations using ...
3
votes
1answer
2k views

How to simplify symbolic matrix multiplication results?

I've defined three symbolic abstract matrices X, M and S as shown below. ...
9
votes
4answers
2k views

Minimum spanning Tree from a weighted adjacency graph

Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137658?p_p_auth=8QnKtT9I I have a really big graph, 40x40. Here is my code ...
1
vote
2answers
1k views

Classification of a linear system of equations with a parameter

I need to get every possible value of k that returns infinite number of solutions or no solution to this system: ...
2
votes
2answers
278 views

Keep order of mulciplication in Matrix production

{{λ E, B}, {λ A1, λ E}}.{{E, 0}, {-A1, E}} \begin{align*}\left(\begin{array}{cc} E^2 \lambda -A1 B & B E \\ 0 & E^2 \lambda \\\end{array}\right)\end{...
1
vote
2answers
957 views

Row-Reduced-Echelon-Form with Equation Parameters for Consistent Systems

I often do row-reduced-echelon-form (RREF) calculations that involve parameters using the RowReduce command. Most times, I want to know which parameters make the system consistent. For example: <...
6
votes
1answer
2k views

Fastest way to do vector / matrix multiplication with constant matrix

Suppose we have a fixed n x n matrix, call it $B$. What is fastest way to evaluate $v^t B\;v$ over many different vectors $v$? Since $B$ is a constant matrix, does this allow the number of operations ...
4
votes
1answer
112 views

quadratic constraint feasibility

Suppose that $A$ is an $n \times n$ matrix, and I have observed some entries of $A$, say, $A_S$ ($A$ restricted on $S$) for some subset $S$ in $\{1,...,n\} \times \{1,...,n\}$. I want to know if it's ...
2
votes
3answers
197 views

Any way to reverse span and join two span in Mathematica?

I port a matlab code to mathematica. In the original matlab code, I use ":" to pick up the desired elements in a matrix. In mathematica, I find in the documentation that the span operator is ";;" (...
12
votes
1answer
5k views

Extract matrix from a system of linear equations [duplicate]

I have a big system of linear equations $f_i(x_1,...x_n)$ with $n$ variables and $n$ equations. I want to extract the matrix $M$ where $\vec{f}(\vec{x})=M\vec{x}$. For example if I have $$ f_1(x) = x ...
2
votes
1answer
5k views

Direct sum of matrices [duplicate]

Is there a simple way (perhaps even a built-in function) that allows one to compute the direct sum of two square matrices?
3
votes
2answers
415 views

johansen test error in code

Cross-posted at the Wolfram community forum I have found this code on a forum, apparently it worked in a previous version of mathematica. Now when I run it, it keeps running for ages. I am not able ...
1
vote
1answer
107 views

Matrix generation

I have a $2x2$ matrix $M$. $M$ has the following form: M = {{a, bExp[-2ikz]}, {bExp[2ikz], a}} $a, b, k - const.$ z is ...
7
votes
5answers
227 views

Selecting terms from a matrix

There are similar questions to this on the forum but none fit the purpose here: I would like to extract certain elements of a matrix depending on whether a factor is present or not, and create ...
2
votes
1answer
1k views

Plotting a matrix in 3D With specific ticks [duplicate]

I have matrix and I want to plot it in 3D ...
2
votes
1answer
401 views

Quickly sum over vector outer products

I am trying to do a simple summation over outer products. I wrote the code as straightforwardly as I could, but perhaps there is a more efficient way to do it. ...
6
votes
3answers
432 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 program....
0
votes
1answer
487 views

Parallelize matrix operations

I'm trying to reduce to a minimum the time of some matrix operations. When I don't parallelize and write the code in the most compact form I get the operation done in around 1sec (is this good? the ...
2
votes
1answer
186 views

DirectAgglomerate not working for Large Matrices

I am trying to graphically display a distance matrix with similar elements visually clustered into groups. My original matrix has the elements in a random order so the first thing I do is to change ...
3
votes
2answers
819 views

Is there a way to parallelize the convolution component of EdgeDetect?

Provided an image like - test = Import["http://upload.wikimedia.org/wikipedia/commons/d/d5/Sunflowers.jpg"] We can run ...
14
votes
6answers
912 views

How to find the distance of two lists?

I have two lists as the following: ab = {1, -1, -1, -1, 1, 1}; ac = {1, -1, -1, 1, 1, 1}; How I can find the difference (more precisely, the edit distance) ...
6
votes
2answers
1k views

Faster Eigenvalues with lower precision goal

I compute all eigenvalues of a large matrix, and I decide that the speed is more important than the precision. Then the question is, can I speed up Eigenvalues[] by ...
1
vote
1answer
105 views

Collect the multiple of one determinant?

m = {{2, 6, 4}, {2, 6, 5}, {-3, 6, 6}}; Consider I'm doing calculation by hand. I want to collect the multiple 6 of second column, how to do that? I'd like the ...
1
vote
0answers
51 views

How to divide all rows of a matrix by their row sums [duplicate]

I've got a general matrix K that I would like to divide it's row's by the row sums of the matrix. I could get this going by doing ...
6
votes
2answers
1k views

How to combine elements of two matrices?

Given two matrices m1 and m2, e.g.: m1 = {{a1, b1}, {c1, d1}} m2 = {{a2, b2}, {c2, d2}} How can one obtain the following? ...
5
votes
2answers
870 views

How can I get Mathematica to recognize equality of symbolic matrix expressions?

I have two matrix expressions: X.Transpose[T].Transpose[X] and X.T.Transpose[X] I want Mathematica to recognize that ...
1
vote
1answer
161 views

Trouble carrying out symbolic operations on matrixes

I have some problems. First of all, I declare matrices like below ...
4
votes
1answer
396 views

How to construct this matrix fast?

I write a function which is a matrix as below: ...
7
votes
1answer
2k views

Matrix Rational Canonical Form

Is there a way to calculate the Rational Canonical Form of an $n\times n$ integer matrix using Mathematica? I have been perusing the documentation and web, but nothing so far.
8
votes
2answers
836 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
326 views

Using two color functions in a MatrixPlot

I'm trying to use two color functions within one MatrixPlot in Mathematica. Is it possible to do this? For example, using a very simple matrix: ...
5
votes
5answers
842 views

Creating overlapped block matrices

I'm doing an FEM assignment using Mathematica. (EK1 = {{a11, a12}, {a21, a22}}) // MatrixForm (EK2 = {{b22, b23}, {b32, b33}}) // MatrixForm I don't know how ...
1
vote
2answers
436 views

How do I create matrices with arbitrary list restrictions?

I want to randomly generate a square matrix of dimension n with entries in the list StartingEntries, and also satisfying that for any such matrix M, the matrix Inverse[IdentityMatrix[n] - M] has ...
4
votes
4answers
343 views

Elegant Matrix Combinations

Suppose you have a matrix (mxn), simplified for illustration m= {{a, b, c}, {d, e, f}} And a set of combinations (simplified for illustration purposes but can ...
-2
votes
2answers
351 views

Mathematica not assigning variable correctly

So I have been fiddling with this the last hour and I just can't get it to work. I have 3 matrices of the same size which contain nothing but 0's in a list, I also have 3 matrices of the same size (...
4
votes
4answers
464 views

Generate Non-Singular Matrix of $n\times n$ dimension

I want to create a function that will make an $n\times n$ matrix which is non-singular that will always retrieve the same matrix (meaning that the matrix will not be random each time). I tried using ...
2
votes
1answer
137 views

What is the best way to produce a symmetric semi-definite matrix using as few variables as possible?

As we know, there are only $\frac{n(n+1)}{2}$ variables in a symmetric $n$-dimensional semi-definite matrix. Is it possible to produce a $n$-dimensional semi-definite matrix whose trace is $1$ using ...
1
vote
2answers
925 views

Error using Solve on Matrix Multiplication

I am trying to make a function the will find that value of $x$ in the following equation: $x.a=b$ all values of $x, a, b$ are matrices. The dimensions of $x$ are unknown, but $a$ and $b$ have the ...
6
votes
2answers
2k views

How to generate a random matrix with specific parameters?

I want to use Mathematica to generate a random matrix with given dimensions, entries coming from a finite set, and with a determinant also coming from a finite set. (It's very important that the ...
37
votes
2answers
2k views

eigenvector bug?

Bug introduced in 7.0.1 or earlier and fixed in 10.0.0 I have a fairly simple $3\times3$ complex matrix, $$ M=\left( \begin{array}{ccc} \frac{7}{2}-\frac{i}{2} & -1+i & \frac{1}{2}+\frac{5 i}...
10
votes
7answers
291 views

Custom Matrix product

I have a list: list1 = {{{a1, a2, a3}, {b1, b2, b3}}, {{c1, c2, c3}, {d1, d2, d3}}}; I want an operation that gives me: Is there a built-in way of doing this? ...
2
votes
2answers
1k views

Determinant of a large matrix and solution of a linear equation

I am trying to solve a linear equation in x, where the equation is given by Det[M]==0. The M is a symmetric matrix (dimensions 47x47) with an element equal to x and all other elements are equal to ...