Questions on the manipulation of matrices in Mathematica.
3
votes
2answers
385 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 ...
2
votes
2answers
89 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
133 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?
-1
votes
1answer
62 views
0
votes
0answers
33 views
How could I find the correct values for every array that would lead me to unique summation number for every unique chain? [migrated]
I have 9 arrays, each array has 9 values, I need to get the proper values in every value's position for every array, and that would give my a completely unique summations for every value's chain from ...
0
votes
1answer
121 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
2answers
43 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?
2
votes
1answer
116 views
2
votes
3answers
137 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
371 views
2
votes
2answers
86 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+ ...
0
votes
0answers
47 views
1
vote
0answers
72 views
2
votes
1answer
81 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 ...
2
votes
1answer
44 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
167 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
84 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 ...
4
votes
1answer
116 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
2answers
156 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)$.
...
3
votes
2answers
230 views
I need to multiply a series of matrices
I need to perform a dot product on a large number of 2 x 2 matrices that I have defined to differ by even/odd subscripts (Ex: D-odd=x but D-even=y). The $\Pi$ function will not work because it does ...
1
vote
1answer
62 views
0
votes
0answers
81 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 ...
2
votes
1answer
79 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
2answers
118 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
87 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 ...
3
votes
1answer
63 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 ...
1
vote
0answers
167 views
Matrix algebra vs. PrincipalComponents and Varimax/Oblimin
Using matrix algebra I can calculate loadings and scores from the covariance matrix (data matrix is column centered):
...
0
votes
1answer
78 views
Dynamic List Building and Exporting [closed]
My ultimate goal is to have a text file that contains the following information in the following format exported to a text file:
...
8
votes
3answers
145 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:
...
5
votes
4answers
259 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 ...
0
votes
1answer
143 views
How to use Compile for accelerating matrix multiplications?
I am trying to find the inverse of the matrix $A$
m = n = 500;
SeedRandom[123456];
A = RandomReal[10, {m, n}];
iteratively using the following matrix ...
3
votes
3answers
88 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
41 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 ...
0
votes
1answer
89 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
56 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 ...
4
votes
3answers
104 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
76 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
77 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.
...
1
vote
0answers
83 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 ...
1
vote
2answers
207 views
badly conditioned matrix (General::luc)
With some matrices I am receiving the following message
Inverse::luc Result for Inverse of badly conditioned matrix (M) may contain significant numerical errors.
How can I tell to Mathematica to ...
-4
votes
2answers
75 views
Ploting from Matrix [closed]
I use Import function from excel in order to get my data. My data contains 3 columns.
...
2
votes
2answers
68 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 ...
7
votes
2answers
156 views
Why does my matrix lose rank?
I want to check the rank of a matrix for observability, but Mathematica loses a rank if the matrix contains very large numbers.
Let's say my matrix is
...
9
votes
2answers
215 views
How to extract and compute on the diagonal entities of a sparse matrix very fast?
As could be seen in the following code:
...
1
vote
2answers
99 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 ...
11
votes
1answer
433 views
Eigenvalues and Determinant of a large matrix
Can anybody kindly explain to me what is going wrong regarding a simple problem I have? I can find the eigenvalues of a large matrix using Eigenvalues[], but when I ...
6
votes
5answers
194 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 ...
0
votes
1answer
776 views
Quick Hessian matrix and gradient calculation?
I am absolutely new to Mathematica and I actually want to try implementing a little optimization method .
Long story short assuming I have a predefined two-variable function f(x,y) I want to ...
1
vote
1answer
85 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
521 views
How to use a 3×3 covariance matrix to plot an error ellipsoid?
I have a 3×3 error covariance in Mathematica, but I don't know how to use it for plotting the error ellipsoid. It would be great if you can show me how I can do that for the below covariance matrix:
...
