Questions on the manipulation of matrices in Mathematica.

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2
votes
2answers
701 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 ...
1
vote
0answers
45 views

Sampling from an one-dimensional Wishart [closed]

I searched for a similar question but could not find one. My problem is sampling from an one-dimensional Wishart distribution. The Mathematica specification is ...
4
votes
1answer
94 views

Is it possible to find the vectors that span the nullspace of a large, symbolic matrix

My problem is composed of two parts, a large sparse matrix $L$ ($m$x$n$ where $m=10^3$, and $n=10^5$, with $10^7$ non-zero complex numbers), and a dense, symbolic matrix $F$ ($m$x$m$ where $m=10^3$), ...
9
votes
1answer
576 views

Symbolic scalar-by-matrix derivative

Let's say I want to calculate the following scalar-by-matrix derivative $$\frac{\partial}{\partial A} \text{tr} \left[(\vec X^T A)^T (\vec X^T A)\right],$$ with $\vec X$ and $A$ being a $n \times 1$ ...
5
votes
1answer
111 views

How to do matrix calculus in Mathematica?

I would like to differentiate Ax with respect to A where A is a matrix. Now, obviously, I know the derivative is x but for more nasty expressions, is there a way to differentiate expressions with ...
6
votes
1answer
97 views

Speed up the auxiliary function magicSquare when $n$ is doubly-even

Today, I saw a question about magic square (please see here). When $n$ is doubly-even, namely for Mod[n,4]==0 ...
1
vote
1answer
72 views

Converting the subscript of matrix name to a variable

I want to change indices of matrix name during loop for creating different matrices. For example; ...
0
votes
2answers
75 views
20
votes
2answers
768 views

Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
6
votes
1answer
469 views

Is there any faster way than Eigensystem to diagonalize a Hermitian matrix?

Is there any faster way than using Eigensystem to diagonalize (get all the eigenvectors and eigenvalues) of a Hermitian (self-adjoint) matrix? That would be ...
19
votes
11answers
1k views

Efficient way to build a certain square matrix

For odd n I'm looking for a short and swift way to construct with (f.e.) n = 3 n = 11 ...
11
votes
1answer
392 views

Is it possible to implement symbolic sub matrices?

The accepted answer in the question Symbolic matrices in Mathematica with unknown dimensions provides a functionality to create symbolic matrices which behave pretty much as the name suggests. ...
17
votes
1answer
294 views

Simple Matrix multiplication takes very long

Bug introduced in 10.1.0 and fixed in 10.3.0 I came across some strange behaviour during a computation involving matrices with symbolic values. It is reproduced below. Multiplying a random 30x30 ...
7
votes
3answers
287 views

Can't find the eigenvectors of a simple 2x2 matrix

Bug introduced in 8.0 or earlier and fixed in 10.3.0 Why can't Mathematica find the eigenvectors of this matrix? ...
2
votes
3answers
213 views

Eigenvalues of a large matrix

I want to compute the eigenvalues (and later the corresponding eigenvectors) of an $n\times n$ Hermitian matrix. For this I use {evs, vecs} = Eigensystem[matrix] or ...
6
votes
0answers
64 views

How to instruct MatrixLog to work with singular matrices?

How to instruct MatrixLog to work with singular matrices by ignoring the zero eigenvalues (thus only acting on a subspace orthogonal to the matrix kernel)? I'm ...
14
votes
6answers
1k views

Generating an Ulam spiral

An Ulam Spiral is quite an interesting construction, revealing unexpected features in the distribution of primes. Here is a related topic with one answer by Pinguin Dirk, who has provided one ...
3
votes
2answers
109 views

Given a list of positions in a matrix, get elements within radius r

I have a n x n binary matrix like SeedRandom[1]; mat = RandomInteger[1, {9, 9}]; MatrixForm[mat] I want to create ...
5
votes
1answer
110 views

Evaluating only one column of a $m \times m$ matrix without evaluating the matrix itself

Suppose I have f[x_] := SparseArray[{someRules}, {m, m}]; g[x_] := MatrixPower[f[x], k]; Would it be possible to evaluate only the $n$-th column ($n\neq m$) of ...
6
votes
2answers
154 views

Grouping the list of numbers that have common.

I am working on some simple problem. It is like puzzle.. Let's say I have some list input={{1,1},{1,2},{1,3},{2,3},{3,3},{4,4}} Which means 1 can go and back to ...
2
votes
3answers
62 views

Having a function check a column and perform a task every time an entry satisfies a condition

So I have a matrix (technically a table) points = Table[{x, f[x]}, {x, Range[0, 2, .1]}]; Which gives something like this in matrixform \begin{array}{cc} ...
7
votes
0answers
99 views

Examples of using Mathematica to solve matrix equations symbolically

Suppose we want to solve a linear system like $$\left\lbrack\begin{array}{cc}M& S\\ -S^\mathrm{T}&0 \end{array} \right\rbrack \left\lbrack \begin{array}{c} x\\y\end{array}\right\rbrack = ...
1
vote
2answers
116 views

Partitioned matrix operations

I have a $(2 \times 2)$ matrix whose elements are themselves $(2 \times 2)$ matrices (i.e., a partitioned matrix), e.g: $$ M = \begin{pmatrix} A & B \\ C & D \end{pmatrix}, \quad \quad ...
2
votes
1answer
74 views

Merge two matrices where one may be empty

In a loop, I want to merge two matrices A and B where B is sometime empty. Example: ...
3
votes
1answer
69 views

Large products of a matrix-valued function [closed]

I have a $3\times 3$ matrix valued function $f(x)$ where $x\in\mathbb{R}$. I want to perform the following: $$\prod_{k=a}^b f(k),$$ where $a,b$ are known, but I cant seem to get Mathematica to do ...
-3
votes
2answers
113 views

How to convert a matrix to MATLAB format? [duplicate]

I want to convert the following 16x16 matrix containing the variable n and some integers into matlab programming language: ...
3
votes
3answers
178 views

Permutations of 0's and 1's in a lower-triangular matrix

For a given $n \ge 5$ create every $n$-by-$n$ matrix containing exactly four $1$'s strictly below the diagonal and $0$'s elsewhere.
-1
votes
3answers
106 views

What would be a good way to implement index notation?

So I need to calculate a 3x3 rotation operator (basically a matrix). I have an index-notation expression, and I was wondering if with pre-calculated theta, K1, K2, and K3, could Mathematica compute ...
50
votes
6answers
4k views

Does Mathematica have advanced indexing?

I have two $M \times K$ arrays $L, T$ where I would like to set all the elements in $L$ to zero whenever the corresponding element of $T$ is greater than 15. The ...
0
votes
1answer
557 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
0answers
66 views

Diagonalisation of equations for NDSolve

I have a linear matrix differential equation and I wish to speed up evaluation by diagonalising using eigenvectors. There is an example in Help for finite elements under "swinging beam" that is ...
4
votes
1answer
76 views

Speed up rendering of ContourPlot3D object

Please can you advise me how to speed up the rendering of the following two planes? When I click and drag to rotate the plot, its movement is quite jerky. Presumably it is working harder than I need ...
0
votes
1answer
110 views

Convert code from C++ to Mathematica [closed]

I need to know how to convert the following code in C++ to Mathematica. ...
3
votes
2answers
212 views

How do you create matrices using submatrix building blocks?

Here is a conundrum I am facing. I have $2$ matrix building blocks. In my problem, I associate integer $2$ with $3\times 3$ matrix $A$ with structure \begin{bmatrix} 0& a& 0\\ c& 0& ...
0
votes
1answer
96 views

Plotting a list of Eigenvectors

For my Fractional Calculus course, I was asked to find a matrix that arbitrarily represents the second derivative. This eventually got me a tridiagonal matrix. I was letter asked to find the ...
1
vote
0answers
61 views

Multiply a matrix by a vector [closed]

I have one 3x2 matrix of coordinates in the following form ...
0
votes
1answer
102 views

Element assignment in matrix function

I have to define a function of two variables that yields a high dimensional matrix, with each entry containing a scalar function, that uses its coordinates in the matrix as input. like this: ...
24
votes
3answers
2k views

Cycles of length N in a graph

If I have an undirected graph represented with an adjacency matrix, how can I find all the subgraphs which are a cycle of length N? I don't really know the math nor the programming language well, so ...
0
votes
1answer
156 views

Syntax::sntxf: “…” cannot be followed by “…\MatrixForm” [closed]

I'm trying to create a $3\times 1$ matrix named Pauli but I really don't understand what's the problem of the following code? ...
3
votes
4answers
344 views

Are table headings functional?

Are table headings for aesthetics only? For example, if I have: ...
14
votes
4answers
587 views

Decomposing a matrix with polynomial elements into a polynomial with matrix coefficients

Let's say I have a matrix, $\mathbf{M}$, that is polynomially dependent on a single variable, such as M = {{15 + a^2, a + 5 a^2}, {a - 5 a^2, 2}} and I want to ...
3
votes
1answer
92 views

Interpolation of ListContourPlot3D, Volumetric data (cube file)

I know there are lots of information about this on stack exchange! Data interpolation and ListContourPlot InterpolationOrder for ContourPlot Unfortunately I was not able to find a proper way to ...
7
votes
2answers
166 views

Solve a time-dependent matrix DE using NDSolve

I am trying to numerically solve a time-dependent matrix DE using Mathematica. However, it seems that Mathematica freezes even for two-dimensional matrix equations. For example, we have: ...
-2
votes
1answer
60 views

solve Z of matrix [closed]

x=Cz+(lambda)z x and z are n*1 column vectors C is n*n matrix (lambda) is a scalar it want to solve for z. the hint is z=Iz where I is n*n also C+(lambda) is an invalid expression, but C+(lambda)I ...
3
votes
3answers
914 views

Using Wolfram Alpha-syntax for transpose, etc

Consider this expression: {{0, 1}, {0, 2}, {0, 3}}*Transpose[{{0, 1}, {0, 2}, {0, 3}}] It returns an error in Mathematica but works perfectly fine in Wolfram ...
4
votes
3answers
303 views

Constructing Tri-Diagonal Matrices

Fractional Calculus Course, we are instructed to create an $n \times n$ Tri-Diagonal matrix in the form of: \begin{array} a A &= \begin{bmatrix} 2 & -1 & 0 & 0 & ... ...
0
votes
1answer
47 views

How to create pairwise difference matrix entry?

I have a $16\times 1$ array of integer entries named $H$. How do I create a $16\times 16$ pairwise difference matrix between all entries in array?