Timeline for Does the solution exist in this matrix system?
Current License: CC BY-SA 4.0
19 events
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| Jul 9, 2023 at 11:08 | history | edited | Henrik Schumacher | CC BY-SA 4.0 |
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| Jul 9, 2023 at 11:07 | comment | added | Henrik Schumacher | So there is no occurency of any symbols whatsoever. | |
| Jul 9, 2023 at 11:07 | comment | added | Henrik Schumacher |
I don't understand you. The b that I get is {0. + 0. I, 0.807353 + 0.127872 I, 0. + 0. I, 0.807353 - 0.127872 I, 0. + 0. I, 0., 0., 0., 0., 0., 0. + 0. I, -0.807353 - 0.127872 I, 0. + 0. I, -0.807353 + 0.127872 I, 0. + 0. I, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -0.00173224 - 0.026907 I, -0.0382822 - 0.0843441 I, 4.76335*10^-18 - 5.75795*10^-17 I, -0.0382822 + 0.0843441 I, -0.00173224 + 0.026907 I, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -1.21339 + 0.0781167 I, -1.90178 + 0.863183 I, 0. + 0. I, -1.90178 - 0.863183 I, -1.21339 - 0.0781167 I}.
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| Jul 9, 2023 at 10:56 | comment | added | fhrl |
I think your answer is not correct to isolate the A and b, as there is still the x element such as the aIcoefficient[1] etc. in the b matrix, The correct is that the aIcoefficient[1] should in x matrix.@HenrikSchumacher
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| Jul 8, 2023 at 5:06 | comment | added | Henrik Schumacher | But the fact that the system is degenerate although you seem to expect that it isn't tells me that you might have set up the system incorrectly. Which can mean that you made a simple mistake when typing it into Mathematica or that you overlooked something when you derived it. | |
| Jul 8, 2023 at 5:04 | comment | added | Henrik Schumacher |
You can try LeastSquares[A,b]. If b lies in the image of A, then it picks the solution with the smallest norm. If b does not lie in the image of A, then it first determines the orthogonal projection c of b onto the image of A and then picks the solution of A.x == c with smallest norm.
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| Jul 8, 2023 at 2:13 | comment | added | fhrl |
I understand your meaning and MatrixRank[A]=45 and MatrixRank[A~Join~{b}]=45, and MatrixRank[x]=50, so it means that there is an infinite solution in this system, rather than no solution. Please how to get some solution using Mathematica?@DanielHuber
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| Jul 8, 2023 at 2:11 | comment | added | fhrl | In addition, how to judge whether the rank is lower because of the accuracy loss in the Mathematica calculation process? | |
| Jul 8, 2023 at 2:11 | comment | added | fhrl | (The most important, although we can get some solution from multi solutions, as we have to do the postprocess, for example by adding or dividing using these solutions, so different solutions will generate different final results, how to judge which final result is right, if there are all selected from several right solutions? | |
| Jul 7, 2023 at 19:13 | comment | added | Daniel Huber | "underdetermined" means that your equations can not uniquely determine a solution. If the matrix has not full rank, see the remark of mikado. | |
| Jul 7, 2023 at 16:04 | comment | added | mikado |
In (I hope) simple terms, 5 of your equations are effectively linear combinations of the other 45. These equations either make it impossible to find a solution (think of x+y==1&&x+y==2) or give an infinite number of solutions (think of x+y==1&&2x+2y==2).
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| Jul 7, 2023 at 15:03 | comment | added | fhrl | What do you mean "the equations are underdetermined."?@DanielHuber | |
| Jul 7, 2023 at 15:01 | comment | added | fhrl |
So you mean that the rank of A is smaller than x, so there will be more than on solution in this system? @DanielHuber
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| Jul 7, 2023 at 10:18 | comment | added | Daniel Huber | If A has a null space of 5 it means the Determinant is zero and it does not have an inverse. Therefore, the equations are underdetermined. The best you may get is 45 variables as functions of the 5 additional variables. | |
| Jul 7, 2023 at 9:26 | history | edited | Henrik Schumacher | CC BY-SA 4.0 |
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| Jul 7, 2023 at 9:24 | comment | added | Henrik Schumacher | "So you mean there is something wrong in these equations? " Yes. "Please can you indicate more clear?" No. How much clearer do you want it? | |
| Jul 7, 2023 at 9:16 | comment | added | fhrl |
This system dimension is A: [50x50], and b: [50x1].
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| Jul 7, 2023 at 9:07 | comment | added | fhrl | So you mean there is something wrong in these equations? Please can you indicate more clear? | |
| Jul 7, 2023 at 9:00 | history | answered | Henrik Schumacher | CC BY-SA 4.0 |