Questions tagged [matrix]
Questions on the manipulation of matrices in Mathematica.
3,196
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Accelerating sum over permutations of matrix elements
I am trying to short-cut the use of a CoefficientArrays call by manually calculating the resulting matrix of coefficients myself (this avoids using symbolic arrays ...
-3
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0
answers
25
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General symbolic computations of matrices using Schur complement
Suppose $A,B$ are $n \times n$ square matrices of the form $A = \left[C_{1}\middle|\frac{I}{0\dots0}\right], B= \left[C_{2}\middle|\frac{I}{0\dots0}\right]$. Say $C_{1} \rightarrow a_{i}$ and $C_{2} \...
- 165
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3
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First few smallest eigenvalues of a large dense symmetric matrix
I construct a large (say 2000x2000) matrix M whose entries are real random variables drawn from a certain distribution. Most of these values will be nonzero, so <...
0
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1
answer
95
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Plot eigenvalues of a matrix with two variables [closed]
I am trying to plot eigenvalues E(kx,ky) of the matrix [mat] depends on two variables kx and ky and of course n its dimension , and the matrix elements a, b and c depend on cos(kx) ; cos (ky) and cos(...
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LyapunovSolve does not give me the correct answer
I am trying to solve an equation using LyapunovSolve, but it does not give me the correct answer. The correct answer should be a 6*6 matrix while by utilizing the Dimension command, it shows me {2}.
...
-4
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1
answer
67
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Constructing NxN tridiagonal block diagonal matrix with N is a variable [closed]
Hi please can someone help me writing a program of generating a tridiagonal block matrix with dimension of NxN where N is a variable can be 50, 100, 200, 300...etc , Well I don't know how I'm a ...
- 19
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46
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Solve eigen-matrix equation
When I read an article by Garbe, where have an eigenmatrix
$$B M_i + M_i B^T=\lambda_iM_i$$
and have the following eigenmatrices and eigenvalues:
$$
M_0=\begin{bmatrix} 0 & 1 \\ -1 & 0\end{...
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2
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127
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+50
Speeding and avoiding unwanted crash of nested Table by `NearestNeighborGraph`
I have a code that generates coordinate points for a 2 dimensional lattice. So the coordinates are of the form {x,y}. Now, I generate a graph out of these ...
- 571
2
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1
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82
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Calculating power series of quantum operators on kets
I am using the "Quantum" add-on package to perform some quantum mechanical calculations using SU(1,1) generators. The code that I've developed reads
...
- 655
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41
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How to compile a matrix with mixed values?
Consider some matrix
matrix = {{a,,...,b,...},...},
where a,b are some strings (like "Name"), ... inside the row corresponds to numbers, and ... are ...
- 4,038
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1
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61
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Calculating the matrix product of the elements of a table
I am trying to compute the matrix product of all the elements of a table of the following form :
...
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1
answer
92
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Manipulating a Haar random unitary matrix and computing probabilities
I am new to Mathematica and its many features. Here is a problem that I was trying to model.
Consider a $4 \times 4$ Haar random unitary $U$.
Define by $|00\rangle \langle 00|$ the following matrix:
\...
- 175
4
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1
answer
47
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Proper usage of Assuming statement
I want to evaluate a command under an assumption, and thought Assuming was the right way to go. Suppose we want to calculate a Matrix rank. Following the second ...
- 251
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1
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46
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How to make a matrix a set of variables to be manipulated?
I have the following
f[xx_, xy_, yx_, yy] := {{xx, xy}, {yx, yy}};
f[a_] = f[xx, xy, yx, yy]
but I don't want to write all the variables for future applications, I ...
- 25
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2
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53
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How to make matrix elements variables [closed]
I have the following matrix
mat := {{xx, xy}, {yx, yy}};
I want to be able to manipulate the matrix elements with the manipulate function
...
- 25
0
votes
1
answer
48
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Converting a list of values to a criterion
Say I have a list of 4 integers valList = { v[1], v[2], v[3], v[4] } whose values may or may not be equal to one another. Now I would like to extract all rows from ...
- 1,032
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163
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VectorAround problem
I am trying to replicate an example give here of correlated variables (it's similar to a more complex problem I'm working on).
I've included the example data and method for convenience:
...
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5
votes
1
answer
165
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Efficient computation of a matrix times its transpose
Let m be a huge matrix and say I want to calculate m.Transpose[m].
The result will be a symmetric matrix, and so it feels like ...
- 1,032
2
votes
1
answer
83
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Minimize Sum of Hamming Distances
Problem:
Given an $n \times m$ matrix with binary values $(0,1)$, find a binary vector that minimizes the sum of Hamming Distances to the rows.
Example:
If the matrix is {{$1,1,1$},{$0,0,0$},{$1,0,1$}}...
- 33
3
votes
1
answer
104
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Proof of symbolic matrix
For any n-order matrix A, B, H
$[A, B] \stackrel{\text { def }}{=} A B-B A$
Try to prove：
(1) $\left[k_{1} \boldsymbol{A}+k_{2} \boldsymbol{B}, \boldsymbol{H}\right]=k_{1}[\boldsymbol{A}, \boldsymbol{...
- 1,407
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0
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32
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Power of trigonometric function matrix [closed]
Calculate the m-power of the following trigonometric function matrix (m>0):
$\boldsymbol{A}=\left(\begin{array}{cc}\cos \varphi & -\sin \varphi \\ \sin \varphi & \cos \varphi\end{array}\...
- 1,407
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48
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Droping a row from a matrix [duplicate]
I want to drop a row from a matrix but the output seems to be:
MatrixForm[]
My code:
...
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1
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SemiDefiniteOptimization - The matrix is not symmetric error [closed]
I get the following error,
SemidefiniteOptimization::herm: The matrix {{0.00256497,0.00128248,0.00128248,0.00128248,0.00128248,2.4286110^-17,6.9388910^-18},{0.00128248,0.00128248,-0.0362029,-0....
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3
answers
217
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Plotting resolvent of the matrix
I'm trying to reproduce resolvent plot of circulant matrix, page 59 of Mark Embree's slides
Straightforward solution below, relying on ComplexPlot3D is below. It ...
- 6,163
2
votes
1
answer
62
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Sorting of a list of lists - i.e. list of matrices - what is the order of the sort determined by?
In the documentation we have:
Sort[list] sorts the elements of list into canonical order.
Maybe I am missing something but what does "canonical order" mean for sorting a list of matrices?
...
- 525
9
votes
1
answer
288
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Eigendecomposition of a matrix with a variable
I have an issue with a decomposition of a matrix $B$ that is positive semidefinite and that depends on a parameter $x$. Writing $\lambda_i\geq0$ the eigenvalues and $\psi_i$ the corresponding ...
- 93
5
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3
answers
204
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matrix Crop (remove leading and trailing zeroes in matrix)
I have some matrices that have 0's around them, for example, give such a matrix
MatrixForm[ mat = ArrayPad[{{1, 2, 3}, {0, 0, 0}, {7, 8, 0}}, {{1, 2}, {2, 3}}]]
\...
- 5,102
1
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1
answer
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How to make an inverse operation to `KroneckerProduct[A, IdentityMatrix[m]]` (simplify matrix)?
The operation KroneckerProduct[A, IdentityMatrix[m]] expands the matrix A in the following way (depending on order of ...
- 2,911
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58
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How to untensor a tensor?
What should I do to convert a matrix of matrices to a non-nested matrix?
$\left(
\begin{array}{cc}
\left(
\begin{array}{cc}
{a_1} & {b_1} \\
{c_1} & {d_1} \\
\end{array}
\right) & \left(...
- 2,911
1
vote
3
answers
86
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How can I realize this matrix product (dot product of matrices of different orders)?
The matrix multiplication of square matrices of different order is often claimed to be impossible. Yet, if the order of one matrix is divisible by the order of the other, a natural multiplication rule ...
- 2,911
5
votes
1
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147
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Finding eigenvectors of a symbolic matrix
I have a $2\times 2$ symbolic matrix for which I want to compute the eigenvalues. It is given as:
Clear[a, b, m]
m={{a, b}, {b, -a}}
and it spits out the ...
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1
answer
157
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Matrix Integro-differential equation
I'm trying to solve this integro-differential equation to obtain the density matrix elements $\rho$.
$
\frac{d\rho}{dt}=-i[H_{0}(t),\rho(t)]-A^{2}\Big[H_{1},\int_{t1}^{t}e^{-B(t-s)}\Big(e^{-i\int_{s}^{...
4
votes
1
answer
77
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How can I have Mathematica solve the curve equation when nested functions are involved?
In the context of Quantum Computing, I am investigating curves that illustrate an error propagation during qubit rotations on a Blochsphere (I asked a related question in the same context here and ...
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437
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How to replace anti diagonal elements of a matrix
I want to assign new values to the anti-diagonal elements of a square matrix m with the values of its diagonal elements. For that, I want to make use of ...
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1
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Does converting large 3D matrices to VERY large 2D matrices affect speed of operations done on the matix?
Novice question! Does the dimensionality of a matrix affect the speed of operations performed on it (or the speed of retrieval of values from it) IF the total number of elements in the matrices are ...
- 185
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1
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Convert List to Matrix [closed]
I have the lists in matrix form, as shown in the screenshot fig.2 below. I would like to convert it to pure matrix like fig.1
Edited:
For example:
...
- 143
4
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1
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159
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Nonnegative Least Squares Algorithm (NNLS) [closed]
Can anyone optimize the code below which is developed in an old version of Mathematica (2003) both in terms of efficiency and adaption to the latest versions of Mathematica?
Description of the code:
...
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0
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Solve 2x2 complex unitary matrix with constains using Solve does not work
I have a 2x2 complex-valued matrix,
$U=\pmatrix{U_{1,1}e^{i\theta_{1,1}}&U_{1,2}e^{i\theta_{1,2}}\\
U_{2,1}e^{i\theta_{2,1}}&U_{2,2}e^{i\theta_{2,2}}}$
which I must impose two ...
- 29
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0
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41
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Matrix row addition inside NDSolve
I'm using NDSolve and my variables are matrix elements so that the equations to be solved are in matrix form. Here is the MWE
...
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2
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2
answers
96
views
Solution to a linear equation with minimum rank
Suppose I have a linear equation, $X.M=A$, for given matrices $M$ and $A$. I can use FindInstance to produce a solution $X$.
How can I add the constraint that $X$ has the least rank?
Indeed, I could ...
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0
answers
50
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How to express elemental operations in matrix form?
I ran the following code:
X = Array[x, {5, 4}];
W = Array[w, {4, 3}];
Y = Array[y, {5, 3}];
D[Norm[X.W-Y, "Frobenius"]^2, {W}]//MatrixForm
However, mma ...
- 1
2
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0
answers
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In an element of a matrix, can I refer in an element to its own row or column? [closed]
In an expression inside the matrix, can I obtain the indices of the element where this expression is located? Also, can I refer to other elements of that same matrix, like in spreadsheets?
- 2,911
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2
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How to obtain independent variables from a set of linear constraints
I have a question, how to obtain independent variables from a set of linear constraints. Let me illuminate this by a simple example, we have 5 variables and 3 linear constraints,
$x1+x2+2*(x3+x4)+x5=...
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48
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How to use Manipulate for Finite Differences
I want to improve my code using the command Manipulate and being able to see the calculus of averages as the indexes l and u are moved. I did a simple example of a 4x4 matrix with the boundary ...
1
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2
answers
93
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How can I generate a tridiagonal block matrix? [duplicate]
$$\begin{pmatrix}C&D&&&&\\D&C&D&&&\\&\ddots&\ddots&\ddots&&\\&&&D&C&D\\&&&&D&C\end{pmatrix}$$
I want ...
- 11
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How to export a matrix in mathematica to some format so that I can read it in python using numpy array
I have a matrix in mathemtica which contains numericals and one symbol in it. I am trying to export this matix into some format so that I can able to read this matix in python. Below is the matix:
<...
- 375
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0
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18
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Not getting evaluated output [duplicate]
I just started using Mathematica.
When doing the matrix calculation I encountered some problem, output is not evaluated instead it just gives the input as the output.
Example:
0
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1
answer
38
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Generalised KroneckerProduct that works like Outer[] [closed]
Is there a Mathematica function that works like this:
Function[f, A, B]
where f is a function with two arguments, and ...
- 103
14
votes
1
answer
384
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Is it possible to use the DGEEV and DSYEV LAPACK subroutines in Mathematica?
Here is my problem: I'm diagonalizing some matrices using Eigensystem[] to obtain eigenvalues and eigenvectors and I'm diagonalizing the same matrices using a ...
- 151