Questions on the manipulation of matrices in Mathematica.

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-2
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1answer
69 views

I need to calculate sin[x] series summation for sin[A] where A is a 3X3 matrix

I am evaluating $\sin(A)$ where $A$ is a $3\times 3$ matrix. I have calculated it but now I want to check this with a Taylor series expansion of Sin[x]. What I am ...
3
votes
0answers
118 views

Discriminant of Characteristic Polynomial

I'm doing a calculation which finds the characteristic polynomial of a matrix with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 ...
3
votes
2answers
475 views

Has Mathematica a function to compute the Smith Normal Form?

The Smith normal form is a matrix that can be calculated for any matrix (not necessarily square) with integer entries. See Wikipedia for a more elaborate description. Has Mathematica a function to ...
3
votes
1answer
170 views

Is there any faster way than Eigensystem to diagonalize a Hermitian matrix?

Is there any faster way than using "Eigensystem" to diagonalize(get all the eigenvectors and eigenvalues) of a Hermitian(self-adjoint) matrix? That would be amazing :). Thanks.
1
vote
1answer
94 views

How to place a matrix under controls (sliders) in a Manipulate?

I want to know how I can place a matrix under my sliders. Here is my code: ...
6
votes
4answers
254 views

Counting adjacent elements in a Matrix?

To start, I have a situation where I have some matrix, for example $$ A=\left[ \begin{matrix} 4&2&2&3&3\\ 2&3&1&2&3\\ 3&0&4&0&4\\ ...
0
votes
1answer
66 views

Solving symbolic matrix equation

I have this equation, $$f(x)=Ax-diag(x)(Ax+b)$$, where $x\in \mathbb{R}^n$, $A\in \mathbb{R}^{n\times n}$ and $b\in \mathbb{R}^n$, for which I need to find the zeros. $x=0$ is an obvious solution, ...
0
votes
1answer
192 views

Symbolic Jacobian computation

I have an equation for which I would like to compute the Jacobian symbolically. $$f(x)=Ax-diag(x)(Ax+b)$$, where $x\in \mathbb{R}^n$, $A\in \mathbb{R}^{n\times n}$ and $b\in \mathbb{R}^n$. I am new ...
1
vote
2answers
196 views

Fast randomization of a graph, while keeping the graph connected

I'm looking for a very efficient method for randomizing graph of a given size (N nodes, L links), but keeping them connected. Assume you have the adjacency matrix A of a given connected graph. You ...
1
vote
0answers
167 views

How to extract connected bipartite graph from incidence matrix

I'm trying to extract a connected bipartite graph Bconn from the a given incidence matrix B- I have a matrix representing a bipartite graph - the incidence matrix B (weighted or not is unimportant). ...
5
votes
3answers
827 views

Matrix Multiplication in context of row and column vectors

I've been looking at some matrices in Mathematica and I've noticed something very weird: They're extremely temperamental when it comes to dot products! For example, if I have the following, ...
1
vote
2answers
108 views

How to create automatically some matrices for symbolic manipulation?

I want to create in an automatic way some matrices to do symbolic calculations with them. They look like these: $$ \left( \begin{array}{cccc} a & 0 & b & 0 \\ 0 & 1 & 0 & 0 ...
8
votes
3answers
322 views

How can I complete a correlation matrix with missing values?

I would like to complete a correlation matrix with missing entries, such that the resulting matrix is positive semi-definite. Say I want to find some x and some y in the next matrix that satisfy ...
0
votes
2answers
223 views

Defining a function in terms of matrix elements

Currently trying to use elements from a matrix in defining a function however having some trouble. This is a somewhat simplified version of the problem. Say I have the matrix ...
1
vote
1answer
176 views

How Manipulating a matrix and a graphic in only one Manipulate? [closed]

I have to manipulate a matrix and graphics in one big Manipulate-Block. This way: Manipulate[Matrixform[mat],Graphics3D[]] How can I achieve that? Ok, here my ...
1
vote
4answers
160 views

Efficient replacement of conditional nested Do over elements of a matrix

I have two matrices like these: m1=Table[Random[],{i,10},{j,10}] m2=Table[Random[],{i,10},{j,10}] I want to create a new matrix in which its main diagonal ...
10
votes
3answers
333 views

Zero-dimensional matrices

In a recent Mathematica project, $(n \times 0)$- and $(0 \times n)$-dimensional matrices have suddenly become a frustratingly common edge case for me. For instance, consider the following two ...
0
votes
0answers
74 views

An error in converting matrix to quaternion

Here is an old quaternions package. There is a function named MatrixToQuaternion, References are here Matrix in that document is ...
0
votes
1answer
113 views

Summation matrix

I have problem with summation when it is in matrices. I want to make mathematica compute this: Large X I have added dataset for as well as e. Would anyone be able to show me how to compute this in ...
1
vote
2answers
130 views

How to sort Table/Matrix including legend(Labellings)

I want to sort table including its legend for graph I have table similar to M1 M2 M3 1 5 2 3 1 4 4 2 -10 5 7 11 6 -2 1 ...
1
vote
0answers
141 views

Efficient submatrix swaps for large sparse matrix

I am implementing the 'swap' algorithm for a binary matrix to generate matrix permutations that maintain row and column totals. My problem is that my matrices are large and sparse (e.g., 19774 x 942, ...
1
vote
1answer
120 views

Decomposing a diagonal positive real matrix

I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$: $$E = \left( \begin{array}{ccc} 0 & & & \\ & a & & \\ ...
3
votes
2answers
118 views

Select elements of a Matrix that are the same (or have certain relationship) and return their position and the element itself

I have a matrix and I want to pick the elements that are the same and return their positions and their values. It seems easy to me, but all I know is how to pick elements that satisfy certain ...
12
votes
6answers
602 views

Elegantly split a matrix into positive and negative parts?

I have a matrix $M$ of real components, and I want to split it into two matrices $M^+$ and $M^-$ of the same dimensions as $M$, where $M^+$ contains the positive components of $M$ (the remaining ...
2
votes
1answer
370 views

Calculate mean square displacements for different particles from a excel file

I have the particle movement data in the following format: ...
1
vote
1answer
89 views

Transform list of inequalities into matrix form $A\ x \leq b$

I have a list of linear inequalities, and I want to get it into the form $A\ x \leq b$; i.e., find the matrix $A$ and the vector $b$. Is there any function in Mathematica that can that can do this?
0
votes
3answers
175 views

Determinant of a random matrix consisting of integers

I am trying to implement a function that finds the determinant of a random matrix consisting of integers. This is the code I have written so far, but I am stuck. Suggestions ? I want to find a ...
0
votes
0answers
71 views

I need to draw a direction field and x1 vs t graph for the ode

I have written the following codes and i am able to get to the trajectory but not able to draw the direction field and x1 or x2 vs time plots. ...
0
votes
0answers
185 views

Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
1
vote
1answer
62 views

Multilpe matrix (mxm) and vector (n), wich are unequal, so get a (three dimensional matrix) mxmxn matrix

For example I have this matrix: mk = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} and I'd like it to multiple with this: ...
0
votes
1answer
195 views

How to speed up the computation of a specific array

I am doing some calculations on superconductivity and I REALLY need to speed up the way I calculate one of my arrays. I will put the input to the matrix (of course a tiny toy model of what I am ...
4
votes
3answers
240 views

Approximate minimum degree permutation algorithm in Mathematica

In MATLAB there is a nice implementation of the so called AMD (approximate minimum degree permutation) algorithm named amd (see Online MATLAB Documentation). There is an alternative algorithm called ...
1
vote
2answers
110 views

Add a column to a matrix as a function of the other columns

I was wondering if its possible to add a column to a matrix by a formula that uses all other columns, like this: ...
0
votes
3answers
463 views

Find the number of nonzero elements

How do you find the number of elements in a matrix that are non-zero. For instance, the following matrix has 5 nonzero elements. ...
0
votes
1answer
188 views

Performing matrix multiplications with a list

I have a question in regards to PseudoInverse. I have $A$, an $n\times 2$ matrix, and when I want to compute $(A^T A)^{-1}A$, by using ...
0
votes
2answers
135 views

How to calculate expected return, row by row in matrix? [closed]

Please help me, I'm writing my project and dont know how to solve this big matrix: I have to compute return row by row: 1st row: (18.32-17.14)/17.14 ; (19.17-18.32)/18.32 .... ...
1
vote
1answer
85 views

Transpose a ragged triangular matrix and display as columns rather than rows

I have a triangular list of lists as follows: ...
10
votes
3answers
409 views

Can (compiled) matrix permanent evaluation be further sped-up?

Update  Multiple optimizations that were suggested by members "ssch" and Simon Woods have in aggregate yielded a ~5X code-speedup; and these optimizations now are incorporated in the example ...
0
votes
0answers
112 views

RowReduce : Record of all the row operations for RREF

I read "for what right-hand sides $b=(a,b,c)$ does $Ax=b$ have a solution", but that question pertains to solving for the unknown vector. I'd like a record of all of the row operations required to put ...
1
vote
1answer
385 views

Is there a built-in function to find the adjoint of a matrix?

I've been looking for a function that helps me get the adjoint matrix o a given one, I found that you can get the cofactors of a matrix but only by using the "Combinatorica" package, which I couldn't ...
1
vote
0answers
134 views

matrix with IF/THEN condition

How to generate all posible matrices with some conditions on the elements? I need to make for given $n$ all $n\times n$ matrices $A=(a_{ij})$ with three conditions: I. $a_{ij}=+1$ or $0$ or $-1$. ...
0
votes
0answers
97 views

Need Help with Output/Code Optimization Conparative Statics with System of Equations and Matrices

I have a system of equations (equilibrium conditions) and would like to evaluate how changes of exogenous variables affect the endogenous values. In step 1, I state the equilibrium equations and some ...
13
votes
1answer
406 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
3
votes
2answers
293 views

How can we multiply nested matrices?

If we have nested matrices, such as: $$ \begin{bmatrix} \begin{bmatrix} a_{1,1} & a_{1,2}\\ a_{2,1} & a_{2,2}\\ \end{bmatrix} \begin{bmatrix} ...
0
votes
2answers
138 views

How to insert trigonometric functions into matrices' vector components? [closed]

Is it possible to insert a trigonometric function into a matrix which will be able to be used dynamically, as an element of one of the vectors of the matrix? I'm trying to perform an operation like ...
5
votes
4answers
226 views

Reduce a huge low-rank matrix

I have a huge square matrix, with a lot of zero columns and zero rows: $m=\left( \begin{array}{ccccccccc} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & ...
6
votes
4answers
497 views

Check if a matrix is Positive Semidefinite

I have a question concerning the check whether a given matrix is positive semidefinite or not. In mathematica the function PositiveDefiniteMatrixQ[m] tells me ...
2
votes
2answers
248 views

Covariance of a P x M x N matrix

I have a stack of tiff files. When imported to Mathematica, they form a $P \times M \times N$ matrix, where $P$ is the number of single images in the stack, $M$ is the number of horizontal pixels and ...
1
vote
1answer
205 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...