Questions on the manipulation of matrices in Mathematica.
1
vote
2answers
127 views
Efficient ways to create matrices and solve matrix equations
I am attempting, for the first time, to use Mathematica to do some serious linear algebra. I would like to solve systems of equations of the form $$U_{n n'} f_{n'} = b_n.$$
I have an expression for ...
13
votes
6answers
327 views
Matrix Rotation
If I have a 2 D matrix of any size say
$\left(
\begin{array}{ccc}
72 & 32 & 64 \\
18 & 8 & 16 \\
63 & 28 & 56 \\
\end{array}
\right)$
$\left(
\begin{array}{cc}
72 & ...
0
votes
0answers
112 views
6x6 matrix NullSpace
I'm working with a 6x6 matrix. Whenever I try to find the NullSpace and FullSimplify it, I get the error
No more memory ...
0
votes
0answers
18 views
Symbolic Calculations with formal matrices [duplicate]
I want to make calculations with matrices in the form (for lovers of statistical mechanics, is just the first step replica symmetry breaking)
...
-7
votes
5answers
199 views
Translating MATLAB's cell2mat into Mathematica
How I can define a function in Mathematica such that it acts same as the cell2mat command in MATLAB?
Example (in MATLAB):
...
0
votes
0answers
312 views
Jacobi eigenvalue and eigenvectors algorithm
Suppose we have a symmetric matrix with dimensions n x n. I need to find the eigenvalues and eigenvectors of this matrix using the Jacobi method. I wrote this code:
...
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 ...
-1
votes
2answers
78 views
Convenient methods to sum select rows (or cols) of a matrix? [duplicate]
What are some convenient methods to sum selected rows or columns in a matrix? This question Summing along rows or columns of a matrix only addresses how to sun entire rows or columns ie, by level.
...
4
votes
1answer
66 views
Using the mouse coordinates to index a matrix
I would like to "write" on to a matrix using the mouse. That is, I would like to use the integer value of Locator coordinates (p) to index a matrix. Then, if the mouse button is down, write a 1 in ...
0
votes
2answers
175 views
How to get complement from two matrices?
This is a special case of my question How to do nor on matrices?
...
1
vote
3answers
109 views
Define new number set
May seem strange at first, but can you make mathematica change the value of 0 to 10 and 11 to 1 for all occurrences. Let me explain:
I'm looping through a matrix and for each element, I want ...
0
votes
1answer
133 views
How to do nor on matrices?
Supose I have matrices a b and c like
a = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
b = {7, 8, 9};
c = {{1},{4},{7}};
I want to get ...
1
vote
2answers
86 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.
...
0
votes
3answers
152 views
Matrix Determinant
I have an N by N (N>3) matrix generated from fortran. I would like to find determinant of that matrix using mathematica? I could do this for a 3 by 3 matrix. I can also import the fortran output file ...
4
votes
2answers
530 views
Solving a time-dependent Schroedinger equation
I want to solve the time-dependent Schroedinger equation:
$$
i\partial_t \psi(t) = H(t)\psi(t)
$$
for matrix, time-dependent $H(t)$ and vector $\psi$.
What is an efficient way of doing this so ...
-2
votes
1answer
86 views
Fortran kind of matrix creation [closed]
I want to create the matrix H of dimensions nxn and matrix elements H(i,j). Because of the physical problem I am dealing with, it is necessary to build it in the following not trivial way.
I know how ...
1
vote
3answers
123 views
Convert coefficients of polynomials into a matrix
I have several sets of 5 polynomials of the form:
...
0
votes
1answer
98 views
Get value only from Position
If have the following command
Position[{a, b, a, a, b, c, b}, b]
(* Out[1]= {{2}, {5}, {7}} *)
Is it possible to get only a sequence of values instead of this ...
6
votes
3answers
163 views
Permanent minors
The function Minors yields the minors of a matrix. Is there a function that yields the permanent minors of a matrix?
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:
...
7
votes
2answers
158 views
How to generate a matrix group?
I have three $7\times 7$ matrices (with real entries, lots of zeros) and I'd like to check if they generate a finite group (or, more precisely, if the group they generate is of precise order). Would ...
1
vote
1answer
57 views
Is there a cleaner/shorter way to select-replace in matrices? [duplicate]
I love Mathematica, but I find it oddly lacking when it comes to how matrices are handled. Here is an example of code that works but seems like it should be a lot shorter (and minus the loop).
I'm ...
0
votes
0answers
61 views
Mapping a function to a Matrix [closed]
I’ve looked up previous answers to this question but haven’t found a suitable answer.
I am trying to Map a function that I defined across a Matrix. The function Maps fine across a 1D array but can’t ...
9
votes
2answers
203 views
Speed up 4D matrix/array generation
I have to fill a 4D array, whose entries are $\mathrm{sinc}\left[j(a-b)^2+j(c-d)^2-\phi\right]$ for a fixed value of $\phi$ (normally -15) and a fixed value of $j$ (normally about 0.00005). The way ...
0
votes
1answer
96 views
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 ...
0
votes
1answer
63 views
Why does Eigenvalues[matrix I defined] not work? [duplicate]
This is the code I have in my mathematica notebook. I want to find the eigenvalues of the matrix I created called Hmatrix as defined below. However when I type Eigenvalues[Hmatrix] I get the Hmatrix ...
-1
votes
1answer
121 views
An issue regarding Eigenvalues function [closed]
Can anybody please kindly explain to me why the members of the output vector produced by the following example are not equal to zero?
...
3
votes
1answer
136 views
How to get the determinant and inverse of a large sparse symmetric matrix?
For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
1
vote
3answers
169 views
How do I create a matrix of functions?
I'm trying to create a matrix in which the elements are functions of two variables, but I can't figure out how to do it. Is it possible? The only way I could figure out is to define the matrix in ...
1
vote
1answer
82 views
Importing a matrix from a text file
I have a $4 \times N$ matrix in a .txt file of the form:
-17.071 137.567 16.554 0.65
-16.873 136.138 16.934 0.7
-15.397 135.738 16.894 0.7
-14.7 135.982 15.9 0.6
...
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
...
4
votes
2answers
216 views
All possible solutions to the Matrix Equation (free variables appearing)
I am attempting to solve a system of linear equations using LinearSolve[] . In my case, the number of unknowns are more than constraints. I learnt that LinearSolve ...
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
...
19
votes
1answer
915 views
Is there a way to convert an image into a Graph?
I'm trying to convert an image with several overlapping dots into a Graph. The goal is to be able to derive the Kirchhoff matrix for the randomly created "network ...
1
vote
1answer
66 views
Confirming the existence of a function related to a matrix
Is it possible to get an answer to the following question in Mathematica?
Let $M$ be a $n$ by $n$ matrix, is there a function $m:\mathbb{N}\times \mathbb{N}\rightarrow \mathbb{Z}$ such that ...
4
votes
2answers
136 views
How to use “Drop” function to drop matrix' rows and columns in an arbitrary way?
The built-in function "Drop" can delete a Matrix's row and column.
Typical syntax for "Drop" is as follows:
Drop[list,seq1,seq2...]
But what if I want to drop a ...
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
...
6
votes
1answer
102 views
How to calculate only four elements per column in a block matrix?
I have a matrix generated like this :
Table[Sequence @@ {f[t[[i]], j, x], g[t[[i]], j, x]}, {i, 16}, {j, 3}]
where $f$ and $g$ are two different functions, $t$ ...
7
votes
3answers
126 views
Multiply a list of matrices by a list of vectors
How does one multiply a list of matrices by a list of vectors, elementwise? For example, multiplying
...
0
votes
0answers
110 views
How Simplify and Assume can be combined on matrix products?
What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
9
votes
1answer
113 views
inverse of abstract matrix
If you assume the matrix $A$ is invertible, then $A^{-1} \cdot A = I$.
Is there an assumption for invertibility in Mathematica 9? How can one make the following evaluate to the identity matrix $I_3$?
...
3
votes
3answers
205 views
How to transform and swap columns of this matrix in a simple way? Version 2
So, earlier today I asked the question
How to transform this matrix & swap its columns in a simple way?
and was given useful and elaborated answers. Now, I'm still not used to the "Array", ...
14
votes
2answers
358 views
How to form a block-diagonal Matrix from a list of matrices? [duplicate]
like this:
I know join[...] works, but it is a bit troublesome for multiple matrices.I tried DiagonalMatrix[...], but DiagonalMatrix can only form matrix from a list of elements.
3
votes
4answers
227 views
How to transform this matrix & swap its columns in a simple way?
I would like to transform matrix $\mathbf A = \begin{pmatrix} a&b&i&j\\ c&d&k&l \\ e&f&m&n \\ g&h&o&p \end{pmatrix}$ into matrix $\mathbf B = ...
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 ...
0
votes
1answer
109 views
Discrete 3D plots of median ratios of two 2D matrices of lists of values
Lets say I have 2 2D arrays where each cell contains a list of values:
Example:
...
0
votes
0answers
42 views
Inverting a matrix [duplicate]
Possible Duplicate:
Why does MatrixForm affect calculations?
I am facing a strange behaviour from Mathematica when asking it to invert the following matrix:
...
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 ...
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 = ...
