Timeline for Solve the vector-matrix equation. Minimize the length of the desired n-dimensional vector
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2019 at 10:45 | history | edited | J. M.'s missing motivation | CC BY-SA 4.0 | added 147 characters in body; edited tags |
| Nov 15, 2019 at 20:00 | vote | accept | ayr | ||
| Oct 12, 2019 at 18:42 | answer | added | Daniel Lichtblau | timeline score: 9 | |
| Oct 12, 2019 at 16:41 | comment | added | ayr | mikado, I see that the solution to the problem is built around operations with the matrix M? Am I interpreting your words correctly? At the same time, I see the operations of "diagonalization" by the orthogonal matrix. But what is “rotate the solution with the orthogonal matrix” and how does the “eigenvector mentioned above” come from, I don’t understand? As a result, I can’t get the whole picture. Could you show your analytical calculations? | |
| Oct 12, 2019 at 14:35 | comment | added | mikado | In outline, a symmetric matrix can be diagonalised with an orthogonal matrix. You can easily solve the problem for a diagonal matrix. You then rotate the solution with the orthogonal matrix (giving the eigenvector mentioned above). | |
| Oct 12, 2019 at 14:11 | comment | added | ayr | I have already solved this problem with the help of Mathematica optimization modules. But, i want to get an analytical solution. | |
| Oct 12, 2019 at 14:07 | comment | added | Henrik Schumacher | This can be formulated as a a minimization problem with quadratic objective function and quadratic equality constraint(s). I do not think that this can be boiled down to a single linear system of equations. But it can be solved, e.g. by Newton's methos. You might want to use FindMinimum for that. | |
| Oct 12, 2019 at 13:17 | comment | added | ayr | Hello, mikado. Thank you for your response. Did i understand you correctly that i need to find the eigenvectors of the matrix M and choose from them the one that corresponds to the largest eigenvalue? I would like to understand why this is so, because am i new to this section of mathematics? Will this be a global solution? P.S. Yes, C can be negative - why should this be taken into account? | |
| Oct 12, 2019 at 12:28 | comment | added | mikado | Note that you can replace M with a symmetrical matrix that gives the same result. Your solution is given by the eigenvector corresponding to the largest eigenvalue. You might need to think further if C could be negative. | |
| Oct 12, 2019 at 4:31 | history | edited | ayr | CC BY-SA 4.0 | added 503 characters in body |
| Oct 12, 2019 at 4:23 | history | asked | ayr | CC BY-SA 4.0 |