Questions tagged [matrix]
Questions on the manipulation of matrices in Mathematica.
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Derivative of matrix functions in NCAlgebra
I mean the differentiation of complex expressions of this type, where the matrices are implicitly given, but it is known that they are a function of vectors. For example:
$q_1=x^TA(x)x$
$q_2=x^TA(y)x+...
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3
votes
1
answer
108
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How do I create and combine column matrices from lists
I need to input the following list of values for x and y , each as a column matrix (7-row, 1-column). Then, combine the two into a 2 x 7 column matrix. I'm new to Mathematica. Please help. How do I do ...
- 133
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Is there a way to apply a two-argument function to matrices?
Basically, I want an analog of MatrixFunction but such that it can apply a two-argument function to two matrices.
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What is the 3rd additive compound of a general $5$x$5$ matrix? [duplicate]
How would I construct the 3rd additive compound of a general $5$x$5$ matrix?
$$A=
\begin{bmatrix}
a_{11}&a_{12}&a_{13}&a_{14}&a_{15}\\
a_{21}&a_{22}&a_{23}&a_{24}&a_{25}...
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1
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How to approximate a function using B-spline interpolation?
I would like to approximate a simple function of y = sin(x) using 3rd degree B-spline interpolation. The formula is:
where D_j are the unknown real coefficients and B_(n,j) are the basis functions.
...
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2
answers
127
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How does NDSolve treat matrices?
I am having trouble trying to solve a differential equation which couples the elements of a matrix. Let's say I have the following
...
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answer
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NDSolve: there are more variables than equations, underdet
I am working on using NDSolve to solve coupled ODE. The following is the coupled equations. It works fine for sever orders. I used table to generate like 962 couple variables and equations, where the ...
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Derivative of quadratic form in NCAlgebra
I installed the NCAlgebra package in the hope that it contains enough rules for symbolic work with most branch-matrix expressions.
...
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4
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2
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71
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Looking for a efficient way of solving a matrix which is function of some variable
What is the efficient way to solve the matrix having a dependency on some varaible f. I have a simple matrix g which is ...
- 335
0
votes
1
answer
46
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Total Spin Matrix Squared (Casimir Operator)
I am trying to get Mathematica to compute the Casimir operator of a 4 particle system of spin $1/2$ fermions. I have the following code which does not do what I would like it to.
...
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votes
1
answer
63
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Invert a generic n x n matrix
I want to invert a generic n x n matrix. Is it possible to do this with Mathematica?
Consider, as a minimal example, the $n\times n$ matrix:
\begin{bmatrix}1n&0&...&0\\0&2n& ... &...
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Giving a scalar and vector function to ND solve?
I'm trying to solve a coupled system of ODEs using NDSolve. In this system, one function is a scalar and another is a vector i.e. it contains multiple components. <...
- 1
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24
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PSDMatrix completion
How can I write a code which gets as an input a symmetric square matrix X with some (symmetric pairs of) entries marked, and outputs whether there is an assignment of values to the marked entries such ...
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65
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How to matricize a vector?
I am wondering how to represent a vector as a matrix, using specified dimensions. For example, MatrixForm[{a, b, c, d}] gives me a column vector. But I would want ...
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1
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Help with equation within adjacency matrix
(Value R seen within desired matrix equation)
resistance = 0.5;
(L = ???)
identitymat = IdentityMatrix[30];
fullmatrix = ((AdjacencyMatrix[plot])) + identitymat // MatrixForm
p.s. I believe I have ...
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Given a matrix with i = number of rows and j = number of columns how to process (look at all entries ) i,j,k using mathematica
I want to process the matrix using the segment of code that says "i, j, k" and then output a print statement if the condition is met"
My goal is to verify that a relation represented as ...
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3
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Insert a dynamic vector into a matrix
If I have the following dynamic vector
Cs[NN_] :=
Table[{Sin[(2*i - 1) τ], Sin[(2*i - 1) τ]}, {i, 1, NN}] //
Flatten
The size of Cs depends on the integer ...
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Unitary matrix with UnitaryMatrixQ
In the Mathematica help, the following example for a symbolic 2$\times$2 matrix
$\left(
\begin{array}{cc}
a & b \\
c & d \\
\end{array}
\right)$,
with constraints, $c=b^{*}$ and $d=-a^{*}$ ...
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votes
1
answer
61
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How to use "Replace" in matrix? [closed]
I would like to change the form of matrix output, for example:
A = {{1, 0}, {0, 0}};
B = {{0, 0}, {1, 0}};
B.A
This will give me a matrix that is the same as the ...
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2
votes
1
answer
116
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Speed Up the Gelman-Rubin-History function
A bit of background information
I have created a function to calculate the convergence of the Gelman Rubin diagnostic (useful in Bayesian analysis). The function seems to work as I want, however I ...
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votes
2
answers
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Find the maximum value of the minimum eigenvalue of the matrix
There is a $4×4$ matrix $Q$ where $c,d,e,m,n$ are variables.
How to get the maximum value of the minimum eigenvalue of $Q$?
$Q=$ $$\\\left(
\begin{array}{cccc}
\frac{12058305}{23104}-304 c & -849 ...
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0
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Dimension of the dot product - symbolic calculation
With the following code
$Assumptions = {a \[Element] Matrices[{2, 2}]};
Dimensions[{{1, 0}, {0, 0}}.a.{{1, 0}, {0, 0}}]
I get as an answer
...
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11
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How can I construct this matrix?
How can I construct this matrix by MMA?
$\left(\begin{array}{cccccc}1 & 2 & 3 & \cdots & n-1 & n \\ n & 1 & 2 & \cdots & n-2 & n-1 \\ n-1 & n & 1 & \...
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Determine value of parameters in a matrix such that it is unitary [closed]
My goal is, given some vectors, multiply them by some constants and stack them as the columns of a matrix $U$. Then I want to know what are the values of the constants such that the resulting matrix $...
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3
votes
1
answer
133
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Construct Special matrix in mathematica
I want to define $D = [d_{ij}]$ as the $(N+1) \times (N+1)$ lower triangular matrix given by the following recursive definitions:
$$
\begin{aligned}
d_{i,i-1} &= i, \qquad\qquad \qquad i=1,2,\dots,...
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Partial Trace with KroneckerProduct
I have some symbolic expression of the form
X=KroneckerProduct[A,B]+KroneckerProduct[G,F]+...
How can I define a partial trace for this, i.e. a function f:
...
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4
votes
1
answer
68
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Mathematica replaces list of zeros with zero [closed]
Consider the following functions:
f[x_]:= {{Im[x], Re[x]}, {Re[x], Im[x]}};
g[x_]:= {{Im[x],0},{0,0}}
When applying each of the functions to the list of lists <...
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2
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Set of quadratic forms and linear algebra
I have a set of quadratic forms.
$L_{1}=u_1^TJ_{1}u_1$
$L_{2}=u_2^TJ_{2}u_2$
$L_{3}=u_3^TJ_{3}u_3$
where $u_{i=1,2,3}$ - 3$\times$1 vector;
where $J_{i=1,2,3}$ - 3$\times$3 matrix;
I need to pack ...
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votes
5
answers
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How do I flatten a matrix of lists while maintaining the structure of the list?
I have a 2x2 matrix of lists. For example, the matrix I am working with looks like
matrix = {{{a,b,c}, {e,f,g}}, {{h,i,j}, {k,l,m}}}
I want to define a function ...
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2
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47
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How to create a symbolic Matrix for evaluation at specific values
I want to create a symbolic matrix that I can evaluate at the given values of variables.
Definitions:
...
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Imposing constraints on any undefined symbol appearing in a matrix automatically
I want to know how can I can I tell Mathematica that all symbols that appear in an object, e.g. a matrix, obey certain constrains, without having to write these conditions by hand.
More specifically, ...
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34
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Trying to map SparseArray over a defined list, the SparseArray defined with 3 subvalues i want to map the 3rd. subValue(list) over the defined list
I have a SparseArray already defined as following
...
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3
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1
answer
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Trying to add up values into a matrix
first post here.
I'm currently completely stuck and frustrated with mathematica. In retrospective, it might had been a mistake to use it for this, I'm actually considering to somehow export the ...
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61
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Working with matrices problem with MatrixForm [closed]
I'm just trying to set up a Matrix 24 by 24 with indices that start from 0 to 23
...
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votes
1
answer
142
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How to construct this Matrix
A $4\times 4$ identity matrix $\mathbb{I}$ can be written as $\mathbb I=\delta_{ij}\delta_{kl}$.
To construct this matrix, I wrote
...
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2
votes
2
answers
82
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making elements of matrix into integers [closed]
how to make elements in a matrix into integers?
here is my matrix:
...
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1
answer
87
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Efficient iteration of matrix multiplication into a table
Suppose I have a list of matrices $(A,B,C)$ and a vector $v$. I want to construct a table whose elements are sequential applications of these matrices to $v$, i.e., the first entry will be $Cv$, the ...
- 595
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votes
3
answers
360
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Jacobian matrix evaluation at a point [duplicate]
I have a vector function $ f(x,y) = (f_1(x,y), f_2(x,y) ).$ I need to find the Jacobian matrix for $f$ evaluated at the point $(x,y) = (a,b).$
I learnt that I can use something like the following on ...
- 53
2
votes
2
answers
88
views
Proving (or refuting) TU (totally unimodularity) of a matrix nxm
I am new to Mathematica and want to prove the totally unimodularity of a matrix (not a particular one, but for any matrix input).
A matrix A is totally unimodular (TU) if every square submatrix of A
...
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How to calculate the determinant for all the submatrix of a matrix?
I want to calculate (and see) all the submatrixes determinant for one non-square matrix with dimensions nxm.
I know I can get the determinant of a matrix using Det(matrix), but I would like to know if ...
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3
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Thread Matrices, like image channels
The code
With[{matA=Partition[Alphabet[],5],matB=Partition[Range@25,5]},
(* matA and matB are 5x5 matrices*)
MapThread[List,{matA,matB},2]
]
is fairly ...
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2
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How to put a FOR loop in a WHILE loop
I have a strange matrix like this one in the picture
Now, my goal is to change all the 1s with random complex numbers of modulus 1, but if the element $a_{12}=z$, then $a_{21}= \bar{z}$, so the ...
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Solve the current equation with respect to one of the coefficients and substitute it into each equation of the system
Good day to all!
In this question about recurrence relations, I had a simple case when the k + 1th variable is represented in terms of ...
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votes
0
answers
61
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Solve coupled differential equation using Matrix
I am a complete beginner to Mathematica. I am trying to solve the following equation:
$\frac{d}{dt}\rho_t = -0.5* \eta* \Gamma[\rho_t]$, where $\Gamma[\rho_t]$ is a 4x4 matrix whose coefficients are ...
0
votes
1
answer
38
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Reduce expressions into (simplified) matrix and vector forms
I have some computation that results in a rather complicated looking expression that could be much simplified by converting it into matrix or vector expressions. For example, instead of ...
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Adding every entry of two tables
I have to randomly create a polymer (random angle between parts), change a random angle by a bit (delta), and determine the energy difference. RandomAngle contains all the angles and DeltaTable ...
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2
votes
1
answer
94
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Dot Product of Vector with matrix components
In Physics it's common to write matrices in vector components to simplify notation. This commonly occures with the pauli vector $\vec\sigma = \begin{pmatrix}\sigma_1 & \sigma_2 & \sigma_3\end{...
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3
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How to define a matrix product based on a different scalar product
I want to define a product of 3x3 Matrices where the coefficient behave in a different way as usual. I defined the multiplication between coefficient as the function MyScalProd
...
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Fitting data in a matrix
Consider the 'm' matrix: Link to 'matrix.dat': https://drive.google.com/drive/folders/1COdMCCBKq85vMDj6Jrb2qqoUlE9eTk6w?usp=sharing
...
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