Questions on the manipulation of matrices in Mathematica.

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3
votes
2answers
77 views

Perform matrix/tensor contractions more efficiently

Problem: explicit index contractions for matrices using the Sum command take too long, and I want to improve the performance for complicated computations. Let me ...
0
votes
1answer
84 views

problem in solving equation

this happened to me when I try to get (f) which should equal sqrt(3)/2 is there any problem in my formula or what? ...
3
votes
1answer
78 views

Plotting eigenvalues smoothly

I am trying to plot how the eigenvalues of a matrix change by changing a given a parameter t. Of course the ordering of the eigenvalues does not matter mathematically but it does when I want to make ...
1
vote
1answer
61 views

Creating a transformation matrix with respect to given bases? [closed]

Let's say I have a linear transformation $T:V\to W$, along with some bases $\{v_1,v_2\}$ and $\{w_1,w_2,w_3\}$ of each respectively. Let's say all the information I have about the transformation and ...
2
votes
1answer
53 views

Efficiently Invert a Square, Block Diagonal Matrix

I am generating an n x n matrix where n is specified by DIM: ...
3
votes
1answer
53 views

Extending matrix (x,y-axis + data) via Interpolation. Looking for elegant & efficient way to write

Please, feel free to edit the title, if necessary. Hi, this is my code working, but actually, the size of my real dataset is 100x100. So, this is very inefficient way. What would be the most ...
3
votes
3answers
141 views

How can I assign matrix values in below form? [closed]

I want to create matrix as the below fig. shows. How can I do it with a do-loop, for-loop, if-loop, or any other way? Thanks a lot...
1
vote
1answer
77 views

Replacing negative components of a matrix with zeros [closed]

How can I replace the negative components of a matrix with zeros?
0
votes
0answers
23 views

Finding the percent difference between elements of a matrix and a list/vector [duplicate]

I have a large matrix of 24 columns, 11 rows, and a vector in the form of a one column, 11 row table. What would be the best method of finding the percent difference between each element of the matrix ...
1
vote
4answers
141 views

Non-rectangular pick of elements of a matrix

How to pick elements of a matrix that are inside a circle centered at the center of the matrix?
2
votes
3answers
131 views

How to write the Taylor expansion of the sum of several matrices?

When $A$ and $B$ are matrices, we have the following Taylor expansion for the inversion function together with basic information on convergence: $$ ...
1
vote
2answers
60 views

Trouble implementing logarithmic matrix norm

I wanted to write a quick function that calculates the logarithmic matrix norm with respect to the spectral norm. The formula is $$ \mu_2(A) = \lambda_\mathrm{max}\left(\frac{A + A^T}2\right). $$ So ...
4
votes
1answer
63 views

Creating a tensor from matrices

I have 3 nxn matrices that I'd like to combine into a nxnx3 tensor. Basically, I want a new nxn matrix where each element is a 3 tuple of the elements of the other 3 matrices at that same position. ...
3
votes
2answers
104 views

Matrix Diagonalization programming

I have a very simple problem, with me misunderstanding the use of Modules and Functions in general, in mathematica. I have a function of which I want to input a Matrix, and in the function I want ...
3
votes
2answers
134 views

Summing matrix products

I need to compute a double sum over a weighted matrix product: $L[M]=\sum_{i,j}^{N}\Lambda[[i]]\;\omega[[i]].M.\omega^{\dagger}[[j]]$. $\Lambda$ is a list of with N complex values(weights) and ...
0
votes
0answers
80 views

How to Extract and Rearrange Elements in Doubly-Nested Lists

Hopefully any easy problem for you guys to help me with! I'm currently having an issue with writing some Mathematica code that will extract the each nth element in each array within a matrix, and then ...
6
votes
1answer
453 views

What does it mean when Mathematica returns a zero “eigenvector”? [closed]

For example, I ask Mathematica to compute the eigenvectors of $\left(\begin{array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 5 & -4 \\ 0 & 0 & 4 & ...
1
vote
3answers
81 views

Percent Difference between elements from 2 matrices

If i have a 22 by 25 table of values which depend on n and r, and a list of values that depends on r that is a 22 by 1 matrix, how can I find the percent difference between each element, by row in the ...
0
votes
2answers
53 views

Plotting plane from a matrix or data table

After weeks collecting data I've decided to pass my results through Wolfram Alpha and see what it gets. The results are amazingly useful, specially the plane generated by linear regression. It is ...
3
votes
2answers
147 views

Zigzag ordered encoding of DCT co-efficients

I am doing DCT steganography. I have obtained a matrix of DCT co-efficient. I now want to perform zig-zag ordered encoding. The matrix is as follows ...
3
votes
0answers
78 views

How to force Series[] to compute expansions by considering non commutative multiplication?

I wish to compute the Taylor series expansion of the following iteration method $x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$ up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ...
0
votes
1answer
43 views

Plotting results of 'Do' loop in contour graph

I want to plot the results of a 'do' loop as a contour graph: ...
3
votes
1answer
152 views

How can I optimize the search between two lists, one that is changing length?

I'm trying to identify unique arrays by comparing two lists, one which is growing in length. The number of elements in the list grows as 2^n^2, where ...
6
votes
1answer
118 views

Issue in Det[…] when computing determinants of polynomials?

When I form a matrix of at least size $12 \times 12$ of second order polynomials in $w$ and I calculate the determinant of that, I get something that is a rational expression in $w$. Since the ...
1
vote
2answers
86 views

Plot values of an $m\times n$ matrix on the complex plane with color varying along $m$

Let's say I have a complex valued matrix $\begin{pmatrix}1+I&2+2I&3+3I\\4+4I&5+5I&6+6I\end{pmatrix}$ represented by a list: ...
4
votes
1answer
57 views

How to create overlapped block matrices and simplify the result

This is sort of a duplicate of Creating overlapped block matrices, but the question wasn't fully answered since the OP never returned to clarify. I am using Kuba's answer for FEM, but I have been ...
0
votes
1answer
56 views

Make Function from matrix [closed]

I have a set of excel data (time v temperature). When I extract it to mathematica it creates a matrix. I want to put the temperatures into a function that is time dependent, so is there a way to use ...
0
votes
1answer
120 views

Solving linear system with constraints

I need to come up with a solution for a rather, odd situation. Let's say I have an $M \times N$ matrix called ${\bf A}$, and I would like to solve it for ${\bf x}$ where $b_1 \le {\bf A} {\bf x} \le ...
1
vote
3answers
69 views

How to convert a matrix into a sparse matrix [duplicate]

If I have a matrix: row 1)1 0 0 4 row 2)0 0 0 0 row 3)5 1 0 0 row 4)0 5 0 0 row 5)0 0 0 9 How would I put it in a sparse matrix format: ...
7
votes
1answer
86 views

A few tuples at a time?

I want to generate $n$ by $n$ binary arrays, and then reduce the output from those arrays by performing a number of permutations and eliminating duplicates. The problem is that the number of arrays ...
5
votes
2answers
242 views

Speed-up the computation of this sum of small matrices

Given a matrix mat with a large number of rows (a few thousands) and a few columns (between 2 and 10), I'd like to compute the sum of the "small" matrices obtained ...
0
votes
0answers
44 views

Problem with stress transformation using InputField [duplicate]

I want to write a code for application of the transformation matrix onto a second-order stress tensor. I have a problem with showing the results. My steps are as follows: 1) I create a Grid with ...
-3
votes
1answer
46 views

Singular matrices with index 1 [closed]

If $A\in \mathbb{R}^{n\times n}$, the index of $A$ is the smallest integer $k$ such that $rank(A^{k+1})==rank(A^k)$ I want to find a singular (id est $\det(A) == 0$) and non symmetric matrix $A$ ...
1
vote
2answers
52 views

Importing data, then plotting ListPlot. What's the most efficient way to write a code?

It should be a boring question to ask for someone, but this is very basic need which I haven't resolved by myself. I know I can use MapThread and pure function to make it short and beautiful, but even ...
14
votes
6answers
410 views

Given a large binary matrix, find the largest submatrix containing non-zero elements

I'm looking for a way to reduce a binary matrix containing zeros at some positions into a matrix that contains no zeros by deleting rows and columns of the original matrix until only non-zero values ...
1
vote
1answer
38 views
9
votes
4answers
244 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
72 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
118 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
60 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
67 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
278 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
77 views

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

I have the following matrix elements: ...
2
votes
2answers
121 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
378 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
250 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
149 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
421 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
102 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
44 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 ...