Questions on the manipulation of matrices in Mathematica.
3
votes
3answers
133 views
Need Help Writing (a Pascal) Matrix in Mathematica
I want to write a function $f[n]$ in Mathematica which gives me an $n\times n$ lower triangular Pascal matrix with a row of zeros in between each nonzero row. That is, I want the matrices
...
3
votes
2answers
243 views
A dot appearing after a zero, and making the entries of a matrix into fractions
For more info about the difference between 0. and 0
I am a self-taught Mathematica user and I have some elementary questions-- perhaps too elementary for this site, but here they are.
If ...
3
votes
1answer
386 views
stationary distribution of a transition matrix
How can I solve the stationary distribution of a finite Markov Chain? In other words, how can I estimate the eigenvectors of a transition 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 $r_i$ ...
3
votes
2answers
569 views
How to substitute numeric values in a symbolic Jacobian matrix?
I have a multi-variate function from $\mathbb{R}^n\to\mathbb{R}^n$. Choosing any desired initial vector, we can produce the corresponding function value, which is a vector as follows. The main problem ...
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 ...
3
votes
1answer
229 views
Efficient method for inverting a block tridiagonal matrix
Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix?
For example:
...
3
votes
1answer
304 views
TensorContract of inverse matrix
Matrix inverse in mathematica
If $A$ is an invertible $n \times n$ matrix, then $A\cdot A^{-1} = I$.
To get this statement in Mathematica, you need the assumption
...
3
votes
1answer
66 views
Efficiently finding the maximum value of a column in a matrix
Imagine I have a matrix of the following form:
TestArray = $((a_1,b_1,...),(a_2,b_2,...),(a_3,b_3,...),...)$, where a specific example might be:
TestArray = ...
3
votes
0answers
65 views
Is it possible to lower the bitwidth of (floating point) numbers?
The answer to this question will most probably be a definite no. Nevertheless, I would like to know whether it is possible to represent reals in the memory on less than the standard 32 or 64 bits ...
3
votes
0answers
72 views
How to accelerate updating some parts of sparse matrices?
I am trying to update some parts of an specific matrix as rapidly as possible. In what follows, I first set up the basics things that I want to use
...
3
votes
0answers
154 views
Mathematica Complains about Non Symmetric Covariance matrix, when it's not the case
I was doing some fitting with Mathematica7 using NonlinearModelFit. It's quite long the program to do the fit and that's why I am not displaying here ...
It goes ok, and I can get the fit parameters ...
3
votes
2answers
386 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
3answers
577 views
Orthonormalization of non-hermitian matrix eigenvectors
When using Orthogonalize[] one can specify which definition of "inner product" is to be used. For example, ...
2
votes
3answers
145 views
MatrixForm explanation as why row extract is displayed as a column?
I have a 5 x 5 matrix:
cdsSpread5yrs =
But after doing a row extract, why is it displaying as a column?
...
2
votes
3answers
408 views
Finding eigenvalues of a $1500\times1500$ matrix
I need to find the eigenvalues of a $1500\times1500$ real symmetric matrix given by $A_{i,i+1}= A_{i+1,i}=-1$ and also $A_{1,N=1500}=-1$ (this is because of a periodic boundary condition used) and all ...
2
votes
3answers
141 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
2answers
135 views
How can I shift the frame ticks to the corner of each element-cell in a Matrixplot?
I am using the following code,to create a Legend for my plot. I would like to shift (or re-position) the frameticks to the corner of each of the cell-elements instead of being in their middle. I ...
2
votes
1answer
122 views
How to modify a matrix to satisfy a special condition?
I have matrix like this:
How do I modify this matrix to make it satisfy the following condition:
For each element {i, j} in the matrix the sum of the elements of row i must be equal to the sum ...
2
votes
5answers
120 views
Test First row of matrix
What is a good way to test the first row of a Matrix to check if one of the values equal a value. For instance, In this example, I want to get vector in the second row that has the bigger value in the ...
2
votes
3answers
573 views
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, $\vec \sigma \times \left( {1,2,3} \right)$.
...
2
votes
3answers
271 views
2
votes
1answer
141 views
Solving an equation involving a determinant
I have a matrix which doesn't include numerical values. There are four variables in it. It is defined by
...
2
votes
1answer
199 views
2
votes
1answer
127 views
Numerical comparisons of matrices
I have a matrix which should be equal to a null matrix. However due to the numerical precision, a brutal equality test with a matrix initialized with zeros does not work.
How should I perform the ...
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 ...
2
votes
2answers
91 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).
...
2
votes
1answer
117 views
2
votes
2answers
87 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+ ...
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 ...
2
votes
1answer
38 views
Replace a specified portion of an array with elements from another smaller array
This may be a trivial question, but I have been at it for a couple of hours and I have not made much progress.
I have a 10 x 10 array (T) that I have used to generate an 8 x 8 array (Q). I want to ...
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
181 views
Tridiagonal matrix for any n
I'm pretty new to Mathematica and I need to figure out how to create a $n\times n$ tridiagonal matrix for any $n$. I don't have the slightest clue where to begin.
Edit: got this far, not sure how to ...
2
votes
1answer
131 views
Creating a matrix from the output of a variable inside a for loop
I would like to enter the results of the following loop inside a matrix as its elements:
...
2
votes
2answers
535 views
Matrix multiplication in Block Form symbolic calculation by Mathematica
I have a problem which requires taking product of two $10\times10$ matrices. I would like to do it by considering both matrices as $5\times5$ matrices such that each entry of both matrices is actually ...
2
votes
1answer
158 views
Different determinants on 2 different computers
Is there any way to force Det to do itself in a certain way?
I've been running the same notebook on 2 differents computer, one MacOSX Lion and one W7 (both 32bit) ...
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 ...
2
votes
2answers
296 views
Total Variation Distance of probability matrix
How can I calculate the Total Variation Distance of a transition Matrix? is there any built in function? I've searched all documentation and haven;t found anything.
** More information:
Let me try ...
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 ...
2
votes
1answer
130 views
Can I reduce a matrix inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$?
I'm new to Mathematica. When I do linear algebra, I wonder if I can have an inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$, where $\mathbf x$ is a column vector ...
2
votes
1answer
371 views
1
vote
3answers
212 views
How do I combine the data from two tables according to a rule of my own devising?
I have two matrices a = m x 5 and b =m x 5 (m is large, say 1,000) which are already sorted as below:
How to generate a new matrix c = m x 5 which consists:
Column 1: exact replica of Column 1 ...
1
vote
2answers
135 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
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 ...
1
vote
3answers
145 views
More than one expression in the Table[] command?
I would like to construct a Matrix using the Table[] command. The issue is that I would like to use more than one expression for it. What I need to obtain is something like this :
...
1
vote
1answer
250 views
Matrix Multiplication Modulo 2
I would like to perform matrix multiplication modulo 2. Hence, instead of the usual:
A.B
I did:
...
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 ...
1
vote
2answers
85 views
How do I divide the columns of a matrix by the sum of its elements?
I am trying to create a transition matrix for a network. In order to do this, I need to sum down the column (the out degree), and then divide the column by the out degree in order to normalize it.
...
