Timeline for How to solve a system of quadratic equations?
Current License: CC BY-SA 4.0
15 events
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| Jul 22, 2020 at 16:16 | comment | added | Rodrigo de Azevedo | X-posted: math.stackexchange.com/q/3764350/339790 | |
| Jul 22, 2020 at 0:48 | history | edited | heng | CC BY-SA 4.0 |
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| Jul 22, 2020 at 0:35 | comment | added | heng | @lambda I agree, from $\mathbf{y}$ to $\mathbf{x}$ there's a sign ambiguity even if $\mathbf{A}$ is full rank. Actually in my case $\mathbf{x} > 0$. I want to know whether there are other methods to solve quadratic equations? | |
| Jul 22, 2020 at 0:31 | comment | added | heng | @LSpice Let's say $\mathbf{A}$ is always full rank in this case. I want to know how many quadratic equations are required to obtain $\mathbf{x} \in \mathbb{R}^3$, is p=3 enough? | |
| Jul 21, 2020 at 16:06 | comment | added | Rodrigo de Azevedo | Related: mathoverflow.net/q/308163 | |
| Jul 21, 2020 at 15:48 | comment | added | Rodrigo de Azevedo | Have you tried in $\mathbb{R}^2$ first? | |
| Jul 21, 2020 at 15:40 | history | edited | Rodrigo de Azevedo |
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| Jul 21, 2020 at 15:30 | history | edited | Rodrigo de Azevedo | CC BY-SA 4.0 |
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| Jul 21, 2020 at 13:42 | comment | added | lambda | If $\mathbf x$ is a solution then so is $-\mathbf x$, so you can't ever have uniqueness. Up to sign you can certainly recover $\mathbf x$ from $\mathbf y$ so the condition for having only two solutions is indeed just that the matrix has full rank. | |
| Jul 21, 2020 at 13:42 | review | Close votes | |||
| Jul 27, 2020 at 3:03 | |||||
| Jul 21, 2020 at 13:23 | comment | added | LSpice | What do you mean by "What is the minimal value of $p$ to guarantee a unique solution"? Do you mean the minimal value for which a solution can be unique? No matter how big $p$ is, $\mathbf A$ could be, say, the $0$ matrix, in which case there are no solutions, or some low-rank matrix, in which case there could be multiple solutions. | |
| Jul 21, 2020 at 13:22 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading; deleted "thanks"
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| Jul 21, 2020 at 13:06 | history | edited | heng | CC BY-SA 4.0 |
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| Jul 21, 2020 at 12:05 | review | First posts | |||
| Jul 21, 2020 at 12:23 | |||||
| Jul 21, 2020 at 11:56 | history | asked | heng | CC BY-SA 4.0 |