Timeline for Structures like vector spaces but closed under heterogeneous products
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 13, 2019 at 17:46 | comment | added | Jon Doyle | The terrible acronym was intended to be terrible, to motivate the question about standard or more descriptive names. | |
| May 13, 2019 at 14:56 | comment | added | Najib Idrissi | @JonDoyle No, it's not a free module. Your family of vectors is not linearly independent. For example $(1,0) \cdot (0,0,1) = (0,0,0)$. (Also, as all French people I love acronyms, but FMOCRNSBFCPEM is just too much.) | |
| May 13, 2019 at 14:50 | comment | added | Jon Doyle | Consider $R^2 \times Z_2$ over $R \times Z_2$ with scalar multiplication defined by $(a,b) (x,y,z) = (ax,ay,bz)$. Is this not a free module with linearly-independent basis $(1,0,0), (0,1,0), (0,0,1)$? | |
| May 13, 2019 at 14:47 | comment | added | Jon Doyle | I edited the question to clarify the points raised by Lspice and McLaury, and to provide some additional information. | |
| May 13, 2019 at 14:26 | history | edited | Jon Doyle | CC BY-SA 4.0 |
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| May 13, 2019 at 13:58 | comment | added | lambda | $\mathbb R^m \times \mathbb Z_2^n$ is not a free $(\mathbb R \times \mathbb Z_2)$-module unless $m = n$. | |
| May 13, 2019 at 12:47 | comment | added | Daniel McLaury | 1. According to the definitions I see online, the field of scalars of a pseudo Euclidean vector space is taken to be the reals by definition. 2. What to you mean by a pseudo Euclidean metric here other than the nondegenerate bilinear form itself? | |
| May 13, 2019 at 11:14 | history | edited | Jon Doyle | CC BY-SA 4.0 |
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| May 10, 2019 at 15:27 | comment | added | LSpice | What is a pseudo-Euclidean space? What is a mechnical property? Aside from the fact that the ground ring $\mathbb R \times \mathbb F_2$ is not a field, what properties is $\mathbb R^n \times \mathbb F_2^m$ missing that $\mathbb R^n$ and $\mathbb F_2^m$ individually both have? Would you expect $\mathbb R^2$ as an $\mathbb R^2$-module to be an example of your kind of structure? Why is PEFMOCR and not FMOCRNSBFCPEM the abbreviation for your property? | |
| May 10, 2019 at 13:24 | history | asked | Jon Doyle | CC BY-SA 4.0 |