Questions on the manipulation of matrices in Mathematica.

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1
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1answer
42 views
9
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4answers
256 views

How to convert a sparse matrix to a list of sparse arrays?

I have a matrix stored as a SparseArray. How can I convert it to a List of its rows, where each row is stored as a ...
1
vote
2answers
73 views

Is it possible to draw a line on a MatrixPlot that would reflect density of row values? [closed]

I have a MatrixPlot with some data and I'd like to draw a vertical lines representing the "average" (density) of that data for each row. Something like this for ...
5
votes
3answers
119 views

Finding most general matrices $A$ and $B$ such that $A\cdot B=1$

I would like to find the most general shape of matrices $A$ and $B$ such that $A\cdot B=1_{4\times4}$. Naively, I just define for example ...
0
votes
1answer
62 views

Varying constant in Matrix calculation to generate 3D plot

As suggested, I rewrite my code to make it simpler and directly showing the problem. Here is a short example. I'd like to generate 3D plot where x,y,z (= a,b,answer) while I am varying a (0 ...
-1
votes
1answer
68 views

Find inverse of the parametric matrix [closed]

I want to calculate the bellow parametric matric but I faced with this error: any suggestion?? ...
4
votes
4answers
295 views

Constructing a large tridiagonal matrix with alternating signs

What is the best way to construct a large tridiagonal matrix, in the following form (notably with alternating signs)? $\mathbf M = \begin{pmatrix} 0 & a & 0 & 0 & 0 & \cdots \...
3
votes
0answers
80 views

Find the generators and group description of a set of matrices [closed]

I have the following matrix elements: ...
2
votes
2answers
133 views

Repeated multiplication of a square matrix and a column vector in Mathematica

I am very new to Mathematica and StackExchange, so pardon me if I am repeating a question that has already been answered. I am trying to use Mathematica to do the following: u[n+1] = A.u[n] where A is ...
11
votes
2answers
394 views

Expressing the n-th power of a matrix [duplicate]

My matrix is $\qquad A= \begin{pmatrix} {1} & {2} & {3}\\ {4} & {1} & {0}\\ {0} & {5} & {4} \end{pmatrix} $ I need $\qquad A^n$ I tried ...
6
votes
6answers
264 views

How do I build a patterned matrix (high-pass and/or low-pass filter bank)?

I would like the shortest code to build the following matrices, of arbitrary dimension $N$: A Low-Pass filter bank matrix is of the form $ \begin{bmatrix} 1 & 1 & 0 & ...
3
votes
0answers
177 views

Mathematica's Singular Value Decomposition different from another math engine [closed]

I’ve been working with SVD – singular value decomposition. Things weren’t working as expected. Thus, I looked over to Matlab and executed the following code: ...
3
votes
2answers
655 views

How do I get the inverse of a homogeneous transformation matrix?

I want to get the inverse of this homogeneous transformation matrix: iab = { {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 3}, {0, 0, 0, 1} } ...
9
votes
1answer
109 views

UnitaryMatrixQ function not returning true for a unitary matrix

So I know this matrix is unitary. It's a well proven fact in quantum mechanics and you can even check for yourself on pen and paper, Heres a quick proof: Assume $H$ is hermitian (i.e. $H^\dagger=H$) ...
1
vote
1answer
46 views

Array Flattening arrays of matrices given by rules

Fix an $n$ and an $m$ positive integers.I have some set of four $n\times n$ matrices $A$,$B$,$Y$,$Z$ (where $Z$ is the zero matrix). I'd like to input the $nm\times nm$ matrix of block matrices given ...
1
vote
2answers
121 views

Update: Calculate Tensor products and traces with Mathematica

My goal is to algebraically simplify expressions involving tensor products and taking the trace. That is, I would like to compute $\operatorname{Tr}\left( \prod_i(id+a_i \otimes b_i) \right)$, using ...
12
votes
7answers
644 views

Brackets around each item in matrix

I have a matrix where every item in the matrix has its own brackets that I do not want. How can I remove the brackets around each item?
1
vote
0answers
29 views

MatrixForm in Mathematica [duplicate]

I wanted to do subtractions between to matrices and I did the following ...
0
votes
1answer
79 views

what do those signs #1, #1^2, #1^3, & mean here? [duplicate]

I have read common pitfalls page and the documentation page but I still don't understand what do those signs mean here? ...
-7
votes
2answers
70 views

How to solve for the eigenvalue in matrix? [closed]

For which value of $a$ in the matrix {{a,2}, {3,4}} has the matrix eigenvalue of $0$? How to solve it in Mathematica?
3
votes
1answer
78 views

Calculating products of given length of two matrices

I have the following problem to solve. Let us have two given square matrices $A$ and $B$ of the same size and a positive integer $n$. I would like to produce all products of length at most $n$ of ...
7
votes
1answer
197 views

Incorrect Left and Right Eigenvectors in Mathematica

I'm trying to find the Left and Right Eigenvectors of a pretty straightforward matrix, but Mathematica doesn't seem to be able to do it for even a 200 dimensional matrix. Background: Given an ...
4
votes
0answers
176 views

Finding eigenvalues in Mathematica: why so slow?

I am trying to find the eigensystem of a large sparse real symmetric matrix, and I only need the lowest 40 or so eigenstates. The relevant code is as follows: ...
0
votes
4answers
123 views

Constructing an arbitrary dimensional matrix with a certain rule

I want to construct the following matrix $M$ of dimension $(N+1)\times(N+1)$ with the following rule (for arbitrary N). Below, in the subscript, as usual, the 1st index gives the row and the second ...
2
votes
1answer
34 views

Encoding/Decoding matrices as integers, integers as matrices [closed]

I want to convert large binary matrices of m x n dimensions into integers, and then to convert these integers to the original matrices. I attempted the following: ...
1
vote
1answer
65 views

Monitoring a matrix with changeable elements as Manipulate in plotting [closed]

If we remember, Mathematica has an ability to show a Psudo-window of plots for monitoring the effects of some changeable parameters in the functions. For example ...
1
vote
1answer
96 views

diagonalization function

If we have a matrix m which is n*n, how can I do mm=U^dagger m U which is a transformation ...
2
votes
2answers
114 views

plotting eigenvalues with devoted level coloring

I am about to plot eigenvalues of a matrix versus varyingj's. ...
6
votes
1answer
64 views

Constructing a particular Toeplitz matrix with a certain rule

I want to construct a Toeplitz matrix in Mathematica. Usually it is done in Mathematica using the following command: ToeplitzMatrix[{a,b,...},{a,y,...}] I want ...
0
votes
2answers
80 views

Flipping random elements in a matrix

I'm still a beginner with mathematica so maybe the solution is obvious, but for some reason my code that worked fine earlier doesn't work now. I haven't changed anything about it. I've restarted ...
0
votes
1answer
35 views

What is the function “oneflag_:0” in this expression? [closed]

The first function Pivotdown can zero out all entries in a column below a desired location. But l don't know the function of “oneflag _0".
1
vote
1answer
59 views

Generate a simulated covariance matrix

I am working on a problem where one of the input variables is the level of covariance between the entries in a particular matrix. To simulate this problem in Mathematica, I will need to feed my code ...
4
votes
1answer
61 views

Computing the logarithmic spectral norm rapidly

I wish to compute the logarithmic spectral norm of a square matrix $A$, which is defined by \begin{equation} \mu_2[A]=\lim_{t\downarrow0}\frac{\|I+tA\|_2-1}{t}. \end{equation} Hence, I simply code ...
5
votes
3answers
240 views

Make a vector of sums of matrix rows

I have a matrix in Mathematica: ...
6
votes
3answers
288 views

How can I create a random symmetric matrix in this way?

The most straight forward way for me to think about is like this: ...
0
votes
1answer
34 views

Picking some elements of a matrix and generating another matrix [duplicate]

If we have a nested matrix as: start={ {{1, 2, 2, 3}, {1, 1, -2, 1}, {3, 2, 2, -I}, {1, 2, 0, -I}}, {{3, 4, 4, 0}, {1, 1, 4, 1}, {3, 3, 4, -1}, {1, 1, 2, I}} } ...
2
votes
1answer
37 views

wrong result of an iteration related to replacement and comparing

We have two nested matrix and a code for replacement following an equality as: ...
1
vote
3answers
121 views

Conditionally binarizing matrices

I want to (fastly) convert matrices with values that are <= a threshold to binary matrices. I used a call to Binarize, but I don't like the Image and ImageData conversions as they obfuscate the ...
4
votes
2answers
98 views

replacement in a nested matrix

We have a nested matrix m1 = {{{1, 2, 2, I}, {1, 1, -2, 1}, {3, 2, 2, -I}}, {{3, 4, 4, I}, {1, 1, 4, 1}, {3, 3, 4, -1}}}; we must replace the first number of ...
6
votes
0answers
131 views

Why has Version 10.3 precision reduced?

In version 7.0.1.0 and versions 10.0 and 10.1 the following is produced: ...
2
votes
1answer
63 views

Why the curly bracket? [closed]

Why are there the curly braces in the output of DY = {{Cos[ay], 0, Sin[ay]}, {0, 1, 0}, {-Sin[ay], 0, Cos[ay], 0}}; DY // MatrixForm It looks inconsistent ...
3
votes
1answer
149 views

Hasse Diagrams from Adjacency Matrix

Let's say I have a rather large adjacency matrix for a partial order relation. Say an 80x80 matrix. What is the best way to display Hasse diagram? I have tried AdjacencyGraph and it does a not so bad ...
1
vote
1answer
45 views

How to find selected elements of inverse of a banded matrix without inverting it?

Is it possible to find some selected elements of the inverse of a large sparse matrix without inverting it? For example consider this Hermitian matrix (as a general case). ...
1
vote
2answers
91 views

Partial comparison between lists contained in larger matrices [closed]

Please presume we have two nested matrices m1 and m2: ...
0
votes
1answer
52 views

generation a nested matrix with a partly comparison of two other nested matrices [closed]

(this problem is maybe challenging because of its partly comparison) there are two nested matrices: mainmatrix1: ...
4
votes
3answers
215 views

Creating a nested matrix from two lists

I have a matrix and two lists: ...
1
vote
1answer
206 views

Derivative of a symbolic matrix

I need to write an elasticity equations as: {{a*∂/∂x,b*∂/∂y},{c*∂/∂x,d*∂/∂y},{e*∂/∂y,f*∂/∂x}}.{{u},{v}} where a,b,...,f are ...
0
votes
1answer
44 views

Lift and projection method in Least Squares Inverse Eigenvalue Problems [closed]

I need to implement the lift and projection method proposed by XUZHOU CHEN AND MOODY T. CHU in http://www4.ncsu.edu/~mtchu/Research/Papers/lsiep.pdf on page 7 in ...
3
votes
1answer
145 views

How to speed up filling a matrix as much as possible in a loop?

In order to find the solution of an $n\times n$ system of nonlinear equations by the method $x_{k+1}=x_k-D_k^{-1}f(x_k)$ where $D_k$ is an approximation of the Jacobian and defined by \begin{equation}...
0
votes
1answer
62 views

LinearSolve on non-square matrices?

I just came across a strange behaviour for LinearSolve (on Mathematica 8.0.0.0). Consider the following definitions: ...