Timeline for Is there a generalization of linear algebra that allows fractional ranks?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2014 at 22:36 | vote | accept | Mike Izbicki | ||
| Jan 31, 2014 at 2:26 | comment | added | Mike Izbicki | Sorry, the number between [0,1] would be an alternative definition for two rows being linearly independent. Then the rank could take on any real range from [1:n], where n is the number of rows/col of the matrix. That's just one idea I had about how ranks might be generalized. You could potentially have others, e.g. by allowing fractionally many columns in the matrix, but I this seems to make even less sense intuitively. | |
| Jan 31, 2014 at 1:50 | comment | added | Terry Loring | Hello Mike -- You ask first for every number in [0,1] but then for fractional ranks. Wikipedia let's a fractional part be real, but the word made me think of fractions. Are you interested in situations in linear algebra where the generalized ranks are rational? | |
| Jan 31, 2014 at 1:32 | comment | added | darij grinberg | Dimensions of objects in monoidal categories can be arbitrary elements of the base ring, and sometimes this freedom is used: mathoverflow.net/questions/16668/… | |
| Jan 31, 2014 at 1:32 | answer | added | Qiaochu Yuan | timeline score: 11 | |
| Jan 31, 2014 at 1:19 | history | asked | Mike Izbicki | CC BY-SA 3.0 |