Questions on the manipulation of matrices in Mathematica.

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9
votes
2answers
2k views

Badly conditioned matrix (General::luc)

With some matrices I am receiving the following message ...
1
vote
1answer
456 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?
0
votes
0answers
44 views

Eigenvalues of a matrix, rhombus/hash sign [duplicate]

I wanted calculate the eigenvalues of A = {{0, 1, 0, 0}, {a, b, c, 0}, {0, 0, 0, 1}, {d, 0, e, f}} Then assigned the parameters a value ...
0
votes
1answer
138 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 ...
0
votes
0answers
50 views

Construct matrix B from columns of matrix A? [duplicate]

Starting with Mathematica and working with matrices, I am looking for a way to construct a new matrix B from columns of matrix A. For example, matrix a has 8 columns and 4 rows, I want matrix B to be ...
1
vote
1answer
83 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
185 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
188 views

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

I have matrix and I want to plot it in 3D ...
0
votes
0answers
117 views

How does Mathematica solve eigenvalues?

I believe mathematica uses some techniques beyond our book. According to the text book it is not possible to solve eigenvalues of which the matrix has not completely eigenvectors, or of those matrix ...
1
vote
1answer
146 views

Construct an infinte matrix with finite sub-matrices

How can I construct an infinite matrix with finite sub-matrices of the form A = (B0, 0, B1 0, B2, 0 0, 0, B3) where each Bi is a rectangular or a ...
0
votes
1answer
182 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. ...
0
votes
1answer
95 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 ...
4
votes
2answers
151 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 ...
21
votes
2answers
2k views

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

like this: I know join[...] works, but it is a bit troublesome for multiple matrices.I tried DiagonalMatrix[...], but DiagonalMatrix can only form matrix from a list of elements.
-2
votes
2answers
181 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 ...
2
votes
1answer
110 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 ...
0
votes
2answers
197 views

Apply a function to a matrix of vectors [closed]

I have a matrix containing on each position a pair of numbers $(a,b)$. I would like to compute the norm of each vector $(a,b)$ and keep the result in form of a matrix. So basically, I need to apply ...
1
vote
3answers
257 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 ...
0
votes
0answers
86 views

Matrices and Upper / Lower Triangular Factorizations

Does anyone know (I have searched documentation, online and MathSource) if there are ways to coax out the following factorizations from Mathematica? $A = LU$, $LU$ factorization $PA = LU$, $LU$ ...
5
votes
2answers
258 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 ...
7
votes
2answers
399 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 ...
1
vote
1answer
87 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 ...
4
votes
1answer
267 views

How to construct this matrix fast?

I write a function which is a matrix as below: ...
8
votes
5answers
305 views

correct way to map a function on entries down the pages in a 3D matrix?

updated: added another method to the methods I tried below for completion. This is new way of doing it, but most likely not very efficient, did not time it I can only visualize 3D matrices in my ...
5
votes
2answers
354 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? ...
3
votes
1answer
292 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
0answers
34 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 ...
1
vote
2answers
521 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
1answer
115 views

Trouble carrying out symbolic operations on matrixes

I have some problems. First of all, I declare matrices like below ...
4
votes
1answer
290 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.
3
votes
3answers
483 views

Can RowReduce work in this matrix?

The matrix $Q$ with dimensions $n\times2*n*m$ is structured by $$Q=[B|AB|\cdots|A^{2*n-1}B]$$ where $Q$ is an augmented matrix built from a $3\times3$ matrix, $A$, and a $3\times2$ matrix, $B$. I ...
4
votes
2answers
173 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: ...
1
vote
2answers
254 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
239 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 ...
4
votes
4answers
236 views

Generate Non-Singular Matrix of $n*n$ dimension

I want to create a function that will make an $n*n$ 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 the ...
1
vote
1answer
112 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
238 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 ...
4
votes
4answers
341 views

Listing matrices up to symmetry

I am interested in the equivalence relation on N x N binary matrices, in which two matrices are equivalent if one can be obtained by rotating/reflecting the other. I would like to obtain a list ...
0
votes
0answers
51 views

Identify columns of a huge matrix just polynomially many rows chosen at random

I am interested in the following problem in combinatorics $\Cap$ Probability. Let $\lambda \in \mathbb{N}$ be a parameter. Consider a matrix of $2^\lambda$ rows and $2^\lambda$ columns. Each column ...
1
vote
2answers
540 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 ...
0
votes
1answer
282 views
0
votes
1answer
89 views

Why does Eigenvalues[matrix I defined] not work? [duplicate]

This is the code I have in my mathematica notebook. I want to find the eigenvalues of the matrix I created called Hmatrix as defined below. However when I type Eigenvalues[Hmatrix] I get the Hmatrix ...
1
vote
4answers
236 views

converting between forms - symbols/subscripts - matrix products

If I have a vector of the form (xp+y, x+yp) do you have a simple way of creating the following matrix and vector from it: {{p, 1}, {1, p}} * {x, y}, such that ...
8
votes
6answers
209 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 ...
2
votes
2answers
346 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 ...
4
votes
2answers
242 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), ...
5
votes
4answers
177 views

Creating simple table

How do I create a table like this? I find it very hard to create the zero-row and zero-column. Edit: I am looking for a solution where a formula eg. Table or something else is being used. I can ...
1
vote
2answers
311 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in ...
7
votes
6answers
313 views

Assigning row of values to a lower triangular matrix

I want to assign a linear row of values to the elements of a lower triangular matrix, i.e., if the row of values is {1,2,3,4}, then the matrix (4 X 4) should be: ...
1
vote
3answers
318 views

RowReduce for symbolic matrices

I'd like to invoke RowReduce on some matrices with a time parameter. For example consider A = {{1, 0}, {0, t}} If ...