Questions on the manipulation of matrices in Mathematica.

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8
votes
6answers
219 views

Custom Matrix product

I have a list: list1 = {{{a1, a2, a3}, {b1, b2, b3}}, {{c1, c2, c3}, {d1, d2, d3}}}; I want an operation that gives me: Is there a built-in way of doing ...
2
votes
2answers
514 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
4answers
330 views

converting between forms - symbols/subscripts - matrix products

If I have a vector of the form (xp+y, x+yp) do you have a simple way of creating the following matrix and vector from it: {{p, 1}, {1, p}} * {x, y}, such that ...
4
votes
4answers
434 views

Listing matrices up to symmetry

I am interested in the equivalence relation on N x N binary matrices, in which two matrices are equivalent if one can be obtained by rotating/reflecting the other. I would like to obtain a list ...
8
votes
5answers
379 views

correct way to map a function on entries down the pages in a 3D matrix?

updated: added another method to the methods I tried below for completion. This is new way of doing it, but most likely not very efficient, did not time it I can only visualize 3D matrices in my ...
5
votes
4answers
190 views

Creating simple table

How do I create a table like this? I find it very hard to create the zero-row and zero-column. Edit: I am looking for a solution where a formula eg. Table or something else is being used. I can ...
2
votes
1answer
197 views

How to use adaptive precision in matrix computations?

I wish to compute the pseudo inverse of rectangular (or square) matrices by the cubically method of Chebyshev given by $X_{k+1}=X_k(3I-AX_k(3I-AX_k))$ where $X_0=\frac{1}{\|A\|_F^2}A^*$. The procedure ...
1
vote
1answer
183 views

Construct an infinte matrix with finite sub-matrices

How can I construct an infinite matrix with finite sub-matrices of the form A = (B0, 0, B1 0, B2, 0 0, 0, B3) where each Bi is a rectangular or a ...
1
vote
3answers
470 views

RowReduce for symbolic matrices

I'd like to invoke RowReduce on some matrices with a time parameter. For example consider A = {{1, 0}, {0, t}} If ...
7
votes
6answers
370 views

Assigning row of values to a lower triangular matrix

I want to assign a linear row of values to the elements of a lower triangular matrix, i.e., if the row of values is {1,2,3,4}, then the matrix (4 X 4) should be: ...
1
vote
2answers
420 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in ...
2
votes
1answer
1k views

Having Problem with Importing Excel file to Mathematica Notebook?

I have solved some equations and exported the final results, which they are several Matrices, as a EXCEL file ( .Xls ). Now, I want to use these EXCEL files as my inputs to solve some other equations. ...
1
vote
1answer
187 views

Averaging multiple 2D data sets

I have multiple data sets, each of which is a 2D matrix. I want to construct a new 2D Matrix in which each element is the average of that element for all the original data sets. i.e ...
3
votes
2answers
473 views

Matrices and polynomials: MMA 8 vs. 9?

I want a function to take a polynomial from a list, plug a certain matrix T into that polynomial, and return the answer as another matrix. My program uses the applyPoly function suggested by a user in ...
3
votes
1answer
597 views

A rotation-like transform on a matrix

Do not be confused with comments, those are for previous version of the question - Kuba Imagine I have a matrix of the form: ...
3
votes
2answers
408 views

Optimization problem with matrix positivity constraints

Is it possible for Mathematica to parametrically find a local minimum of a given function (say of some variable $x$ where $(a,b,c)$ serve as parameters) subject to the constraint that a given ...
1
vote
1answer
728 views

Computing the fundamental matrix and its monodromy matrix

Assume $\dot x(t)=v(x,t)$ is a $T$-periodic, with respect to $t$ dynamical system. That is: $x\in\mathbb R^n,\quad t\in\mathbb R,\qquad v(x,t+T)=v(x,t)$. Let $x_0$ be a smooth periodic solution in ...
1
vote
1answer
144 views

Manipulate doesn't work for plotting a region where a matrix is positive semi-definite

I'm facing the following problem and would very much like you help. Thanks is advance! I have defined the following 4x4 matrix: \begin{equation} S=\left( \begin{array}{cccc} ...
0
votes
2answers
133 views

Create a Matrix out of two matrices

I have two matrices A = {{a1,a2},{b1,b2}} and B = {{x1,x2},{y1,y2}}. I would like to create out of these matrices a new matrix ...
2
votes
1answer
237 views

How to obtain a Symplectic 4×4 matrix?

I have a problem in obtaining a $2n \times 2n$ Symplectic matrix $T$, with $n=2$. I couldn't find a direct command in Mathematica to achieve this. Conditions: ...
1
vote
3answers
147 views

How can I threshold for a minimum value with MatrixPlot?

Looking at the Options for MatrixPlot, there doesn't seem to be a mechanism for lowerbound threshold - i.e. ignoring values that ...
0
votes
2answers
167 views

Taking averages at certain intervals

I am trying to take averages of a large two dimensional array at certain intervals. For example, for the first row, I want to take K averages of 500 values. Here is what I am trying ...
3
votes
2answers
731 views

Importing data into an array, column by column

I'm building a large matrix having different sized rows consisting of a few columns. The different columns are imported .txt files. Why can't I build the matrix column by column? For example, I ...
4
votes
5answers
215 views

Creation of one column matrix

I want to create an one column matrix with the 1st element to be -1, and all the other elements to be zero. However, I want to be able to make a matrix of this kind with arbitrary dimension, that is, ...
0
votes
2answers
99 views

How can I adjust matrices into the same ItemSize and aligned well in Notebook?

I typed three matrices, but they are not aligned well, and the Items in one matrix are also not aligned well and with differenct ...
1
vote
1answer
98 views

sequence of matrix multiplications

My linear algebra book has questions that are are marked to use math software. There's probably some $50 guide on how to do everything but usually documentation has gotten me through. I've been kind ...
0
votes
1answer
152 views

Sorting a list of triplets by first element of each triplet fails

In the last line of code, I´m trying to order the matrix by the first column. I want to store in the Array t2tlistsorted ( 100 x 3 ), but I can´t. ...
11
votes
3answers
1k views

How can I visualize 6 square matrices as a cube?

I have six square matrices of the same dimensions in a list, for example: ...
0
votes
1answer
75 views

Basic Row Traversal Question

Right now I'm using this For loop to do an operation to each row of a $n \times n$ matrix, I was trying to figure out how to do this with ...
0
votes
1answer
135 views

Finite precision - how to get rid of “near zeros” [duplicate]

I am performing a finite-precision operation on a matrix A which I know precisely; call the result B. The operation is taking ...
1
vote
2answers
227 views

Need an efficient method for finding certain matrices

I am trying to write a function which produces square matrices with certain characteristics. The function should have two inputs: number of the rows, n number of ...
4
votes
3answers
187 views

Output to preserve dot product

I am fairly new to Mathematica and I am faced with a problem. I tried to search for the solution but it seems that I don't know how to formulate the short search request. I need to perform a matrix ...
0
votes
0answers
36 views

Eigenvalues for large matrices without Root-Solution [duplicate]

I read some other questions and tried to implement the given answers but yet, I did not succeed to find proper solutions for my eigenvalues. I hope someone can show me how to do this for this case, ...
1
vote
0answers
106 views

NMaximize with matrix input

I defined function f[x_, fixed_] := {...}. Here x is an $M\times N$ matrix. I want to maximize $f$ with respect to $x$. I have ...
1
vote
1answer
205 views

Hermite Normal Form in “columns” convention

After describing the Hermite Normal Form (HNF), MathWorld explains: The Hermite normal form for integer matrices is implemented in Mathematica as ...
0
votes
2answers
222 views

Most efficient way to sum over matrix products?

I have two lists. The first, coefficientlist, is dense and has dimension {176,176} elements. The second, ...
4
votes
0answers
582 views

Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?

If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
1
vote
2answers
567 views

How to find the position of non consecutive numbers?

Given a sorted table, how can I find the position of non consecutive numbers in the first column of the table? ...
2
votes
1answer
104 views

PermuteSubgraph not working? (Combinatorica)

I am trying to write a code to perform the QAP partialling analysis (here's a paper to know more) but the part in which I "scramble" the graph with PermuteSubgraph does nothing, I am actually not ...
1
vote
3answers
139 views

How to convert a spaceless data into tab delimited

I have a data set in form of:(this is just an example) 1324501020 3241030205 4332020134 the data are stored in a text file (e.g. data.txt) but I need to convert ...
0
votes
0answers
46 views

Difference between matrix rapresentation [duplicate]

I've noticed different behaviour in Mathematica between matrix representation: The matrix a={{1,2},{3,4}} is different from b=a // MatrixForm Why i obtain ...
0
votes
1answer
184 views

Pattern match with Table for matrix dimension check

In Mathematica, often an expression involving matrices will encounter dimension mismatch errors, like we are multiplying a 3x2 matrix to a 3x4 matrix. Below we define a new symbol Dim, which can be ...
3
votes
2answers
349 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
519 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?
3
votes
2answers
359 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?
0
votes
1answer
595 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
3answers
1k 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
411 views
2
votes
2answers
429 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+ ...
1
vote
1answer
213 views