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Solve the vector-matrix equation. Minimize the length of the desired n-dimensional vector

There is the following vector-matrix equation. where C - nonzero constant. [x1 x2 ... xn] - vector of real numbers. M - matrix of real numbers of dimension n x n It is required to find a vector $x$...
16 views

How to minimize the eigenvalues of a hermitian matrix?

Suppose I have a complex hermitian matrix, M[x_,y_] whose eigenvalues must be real.I tried to minimize the first eigenvalue by writing following command:f[x_,y_]:=Eigenvalues[M[x,y]][]; Minimize[f[...
41 views

How can I specify the region for every variable simultaneously in NMinimize?

I want to use NMinimize to find the unknown unitary matrix that solves a (possibly nonlinear) matrix equation. For example, the one that transforms the Pauli matrix ...
109 views

Programming with Mathematica Syntax - Dunford decomposition

I am always amazed while I am reading some solutions of problems in mathematical problems of this site with Mathematica. For instance, look at the problem 48. Whereas I am writing 100 lines of code ...
99 views

Find k largest edges with unique nodes (kind of maximum weighted matching)

I have a weighted graph, and I am interested to find k largest edges with unique nodes. Currently, I do it in the following manner ...
152 views

How to sort Matrix

I am on permutation project, and I have trouble with my result, the sequence of my result is not same with Permutations in Mathematica here the code ...
156 views

Find maximum of the norm of matrix

g = 0.9; H = {{g, I}, {I, -g}}; G = MatrixExp[t*H]; Plot[Norm[G], {t, 0, 20}, AspectRatio -> 1] FindMaxValue[Norm[G], {t, 1}] The matrix has a parameter t. ...
125 views

How to efficiently optimize a strictly increasing linear function over convex set

I am trying to minimize the trace of a symmetric matrix $B$ fulfilling $x^T A_i x \leq x^T B x \ \forall x \forall i$ for given (in general) indefinite symmetric matrices $A_i, i = 1, ..., n$. The ...
54 views

Minimize matrix column totals

I would like to pick up n (2 in example) columns from matrix. The sum/total of these columns should be minimal. ...
139 views

How to improve the speed of NMaximize function

My problem is as follows: Consider a 5*5 matrix Obj with 0 and 1 Obj = Array[x, {5, 5}]; The objective function is: ...
51 views

Specific aggregation of matrix elements

Let us consider the matrix 'x1': x1 = {{1, 2, 3, m}, {4, 5, 6, n}, {7, 8, 9, o}, {10, 11, 12, o}} MatrixForm[x1] From the matrix 'x1' we compute the matrix 'x2':...
594 views

Differentiating functions of vectors/matrices?

I'm dealing with derivatives of scalar functions of matrices and wondering if Mathematica can help me here. The standard approach of expanding it in terms of components is cumbersome. As an ...
64 views

Finding a column from Max comparing each element of two columns; subsequent column used for backward calculation

I have lensp=21; rho=0.975; e1=0; pid= 0.5212; qid=0.4788; tid=10; based on my own calculations I have given vectors of dimension ...
212 views

Defining a function for the construction of a bordered hessian

I think in Mathematica the omission of a function that can create a bordered matrix. This code works ...
86 views

An optimization problem involving the calculation of MatrixRank as a constraint

I am dealing with an optimization problem that involves the rank of a matrix as a hard constraint. I am starting with this simple example ...
67 views

An optimization problem involving the calculation of MatrixRank gets wrong

I was trying to solve an optimization problem involving rank of a matrix and experimenting with a very simple one. A 2x2 matrix which contains only one parameter a11...
318 views

Optimize a parametric matrix to get a lowest possible eigenvalue

This question is a followup of Plot the lowest eigenvalues of a parametric matrix Now I can get the lowest eigenvalue LowEign(t) of the matrix for a given t numerically. When I plot the LowEign ...
537 views

Find the minimum element of a row of a matrix and its column index for each row

I am trying to find the minimum value of a row of a matrix and its corresponding column. Please run the code below. OptV is the matrix that I would like to create which must give the output of the ...
859 views

Indicate minimal path sum

Described on the page: http://www.mathblog.dk/project-euler-81-find-the-minimal-path-sum-from-the-top-left-to-the-bottom-right-by-moving-right-and-down/ It is an example of the solution indicated in ...
701 views

830 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). ...
746 views

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