Timeline for Real matrix rings and associative hypercomplex numbers
Current License: CC BY-SA 4.0
18 events
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| Oct 22 at 14:38 | answer | added | Anixx | timeline score: -1 | |
| Aug 23 at 7:12 | vote | accept | Vertvolt | ||
| Aug 22 at 23:32 | answer | added | Qiaochu Yuan | timeline score: 5 | |
| Aug 22 at 23:15 | comment | added | Qiaochu Yuan | Wikipedia does not require that last condition; it says "where possible..." | |
| Aug 22 at 21:58 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
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| Aug 22 at 21:58 | comment | added | Gro-Tsen | So your question is “does any finite-dimensional (unitary, associative) $\mathbb{R}$-algebra admit a basis of elements whose squares are in $\{-1,0,1\}$?”, is it? Because if this is it, then it would be better to phrase it that way instead of using the term “hypercomplex number”. | |
| Aug 22 at 21:56 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
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| Aug 22 at 21:44 | comment | added | Lefevres | OK so do you agree that there is a question ? | |
| Aug 22 at 21:37 | comment | added | Sam Hopkins | The definition on Wikipedia (en.wikipedia.org/wiki/Hypercomplex_number) is this: "A definition of a hypercomplex number is given by Kantor & Solodovnikov (1989) as an element of a unital, but not necessarily associative or commutative, finite-dimensional algebra over the real numbers. Elements are generated with real number coefficients $(a_0,\ldots,a_n)$ for a basis $\{1,i_1,\ldots,i_n\}$. Where possible, it is conventional to choose the basis so that $i_k^2 \in \{-1,0,1\}$. A technical approach to hypercomplex numbers directs attention first to those of dimension two." | |
| Aug 22 at 21:30 | history | edited | Vertvolt | CC BY-SA 4.0 |
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| Aug 22 at 21:28 | history | edited | Vertvolt | CC BY-SA 4.0 |
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| Aug 22 at 21:25 | history | edited | Vertvolt | CC BY-SA 4.0 |
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| Aug 22 at 21:24 | history | edited | Vertvolt | CC BY-SA 4.0 |
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| Aug 22 at 21:24 | history | edited | Vertvolt | CC BY-SA 4.0 |
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| Aug 22 at 21:20 | comment | added | Sam Hopkins | I didn't downvote, but I don't think this question can be answered because there is no precise notion of "hypercomplex numbers." Or if there is one you know of, you should put it in the question... | |
| Aug 22 at 20:51 | history | edited | Vertvolt | CC BY-SA 4.0 |
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| S Aug 22 at 20:32 | review | First questions | |||
| Aug 22 at 23:49 | |||||
| S Aug 22 at 20:32 | history | asked | Vertvolt | CC BY-SA 4.0 |