Timeline for Checking whether a linear homogeneous system with m equations and n>m unknowns, has m unknowns that are sums with positive coefficients of the others
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 12, 2024 at 7:09 | history | edited | florin | CC BY-SA 4.0 | added 12 characters in body |
| Jul 12, 2024 at 7:02 | history | edited | florin | CC BY-SA 4.0 | added 597 characters in body |
| Jul 12, 2024 at 6:46 | comment | added | florin | @A. Kato indeed, this is a nice clarifying example. For n=2, m =1, the positively representable systems are precisely those with one positive and one negative coefficient. For m >1, the class with precisely one "different" sign in each equation is positively representable, but there are other cases, like the example in the question. | |
| Jul 12, 2024 at 6:36 | comment | added | florin | @Bob Hanlon , I treat each monomials like a single, new variable | |
| Jul 12, 2024 at 4:04 | comment | added | A. Kato | Are you talking about general facts on homogeneous linear equations? Then there is a simple counter-example. Consider the case of n=2 and m=1. The solution corresponds to a straight line passing through the origin. If your "property" is true, then the slope of the line cannot be negative. | |
| Jul 11, 2024 at 19:59 | comment | added | Bob Hanlon | Your rv does not consists solely of variables. Some elements are products of variables. Do you want the products treated as if they were single variables or rather split into the separate variables? | |
| Jul 11, 2024 at 13:09 | history | edited | florin | CC BY-SA 4.0 | added 80 characters in body |
| Jul 11, 2024 at 11:00 | history | asked | florin | CC BY-SA 4.0 |