Questions on the manipulation of matrices in Mathematica.

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5
votes
1answer
129 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 ...
2
votes
3answers
275 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 ...
7
votes
1answer
224 views

How write a new MatrixRank feature with symbolic computation

The current MatrixRank is a slight foolish without any capacity of symbolic computation ,feature of Mathematica, like this: ...
6
votes
0answers
74 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 ...
2
votes
1answer
105 views

Is there a good way to check, whether a small value produced numerically is a symbolic zero?

I have a complicated 4x4 matrix and need to know the eigenvalues. I expect a zero eigenvalue for physical reasons. Giving numerical values first gives me an eigenvalue of $\mathcal O(10^{-15})$. Now ...
3
votes
2answers
134 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 ...
6
votes
2answers
162 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 ...
7
votes
0answers
132 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 = ...
2
votes
1answer
79 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: ...
2
votes
3answers
65 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} ...
1
vote
2answers
151 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 ...
-1
votes
3answers
185 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 ...
3
votes
3answers
183 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.
-3
votes
2answers
121 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: ...
2
votes
3answers
64 views

construct matrix by applying derivatives to another matrix

Say you have a vector like the following ...
3
votes
0answers
78 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
95 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
126 views

Convert code from C++ to Mathematica [closed]

I need to know how to convert the following code in C++ to Mathematica. ...
5
votes
1answer
114 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 ...
1
vote
1answer
154 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 ...
3
votes
2answers
301 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& ...
1
vote
0answers
77 views

Multiply a matrix by a vector [closed]

I have one 3x2 matrix of coordinates in the following form ...
0
votes
1answer
321 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
1answer
122 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 ...
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 ...
7
votes
2answers
301 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
76 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 ...
2
votes
1answer
161 views

Eigenvectors of numerical matrix

I have a large numerical matrix whose eigenvalues are all distinct. In the documentation for Eigenvectors it says: For approximate numerical matrices m, the ...
4
votes
3answers
372 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
54 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?
0
votes
0answers
28 views

LUDecomposition does not give the expected results [duplicate]

Check this example: ...
1
vote
2answers
98 views

DiscretePlot3D: Part specification is neither a machine-sized integer nor a list of machine-sized integers

I want to plot a 3D histogram of a matrix and I am using this line: DiscretePlot3D[lmat[[x, y]], {x, 1, 3}, {y, 1, 3}, ExtentSize -> Full] where ...
0
votes
0answers
62 views

Is tensor argument passing to module expensive?

I wrote a simple module which is supposed to do recursive computation, however it turns out to be expensive even for 300 points. I am not sure why is it slow, all the computations seem to be ...
-1
votes
2answers
85 views
4
votes
2answers
327 views

Maximization in Mathematica using matrix and vector notation

I am trying to solve a simple maximization problem in Mathematica, using matrix and vector notation. ...
2
votes
1answer
136 views

When are sparse arrays effective?

Sparse arrays are not effective in Mathematica 10. More computational time is needed to perform arithmetic operations on sparse arrays. Their size is also bigger than normal arrays. Here is a simple ...
10
votes
2answers
240 views

Analytic determinant of a sparse 25x25 matrix?

I would like to compute the analytic determinant of the following sparse matrix ...
2
votes
2answers
171 views

The Chart of Matrix Eigenvalues : Energy Levels

There is the possibility that this question may have been asked previously, but as we are unfamiliar with the nature of the chart below, we hope to seek a response to this query. Consider a matrix as ...
12
votes
1answer
218 views

Nearest Kronecker Product

Some people (see The ubiquitous Kronecker product by Van Loan) have worked on finding two matrices $\mathbf A$,$\mathbf B$ of specified size whose tensor product $\mathbf A\otimes\mathbf B$ is closest ...
6
votes
3answers
256 views

How to simplify symbolic expressions with KroneckerProduct

Having $X,Y$ being symbols for matrices, I was wondering if there is a way to simplify expressions like KroneckerProduct[X, X] + KroneckerProduct[-X, X] to ...
1
vote
2answers
132 views

LUDecomposition for non-square matrices

How do we go about finding the LUDecomposition for non-square matrices. When i try to input the standard LUDecomposition ...
0
votes
1answer
85 views

Eigenvalues and Eigenvectors Order [duplicate]

Say I have a list of eigenvalues and eigenvectors produced from a matrix $M$ using the command {eig1,eig2}=Eigensystem[M], which will return the eigenvalues with ...
0
votes
1answer
36 views

Variable Definitions and Random Numbers [closed]

I have currently created the following matrix: m={{RandomReal[{0,1}],RandomReal[{0,1}]},{RandomReal[{0,1}],RandomReal[{0,1}]}} In other words, a $2 \times 2$ ...
0
votes
0answers
21 views

Matrix Multiplication and Product [$f$, {$i$, $i_{min}$, $i_{max}$}] [duplicate]

I tried the command Product[f, {i, i_min, i_max}], where $f$ is a matrix here, as a shorthand for a product of arbitrarily many matrices with elements parametrized ...
3
votes
1answer
85 views

Evaluating the product of a matrix sequence [duplicate]

I want to compute $$ \prod_{i=1}^n A_i = A_1 A_2 \cdots A_n $$ where every $A_i$ is a square matrix. When I execute ...
3
votes
1answer
112 views

updating matrix elements based on a condition

I am (still) fairly new to Mathematica and trying to perform some operation on the matrix elements, say for the matrix ...
14
votes
2answers
247 views

Fastest way to sum the upper triangle

I feel like this is an recurring question: if there's a symmetric matrix whose diagonal is not all 0, how could I get the sum of the part of it that's above the diagonal as fast as possible? Small ...
1
vote
1answer
70 views

Matrix issue with NDSolve

I am solving a differential matrix equation with NDSolve. ...
6
votes
2answers
197 views

improving sequence dot operator for matrix rows and plot of Norm-imaginary

I have written a code to Dot a row (conjugate of that) of mm to the next one: ...