Are all collinearity preserving bijections from $\mathbb R^3$ to itself of the form $Ax+b$ for $A \in M_{3\times3}(\mathbb R)$ and $b \in\mathbb R^3$?

score 90 · Answer 8 · 2018-07-25 22:15:09

90

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score 11.8k · Answer 9 · 2018-07-29 13:29:43

11.8k

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score 88 · Answer 10 · 2018-08-02 15:01:10

88

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score 95 · Answer 11 · 2018-08-04 08:39:55

95

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score 95 · Answer 12 · 2026-03-17 09:22:22

95

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score 491 · Answer 13 · 2026-03-24 09:24:13

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score 58 · Answer 14 · 2018-08-12 16:43:36

58

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Is the group generated by $f(x)= x+2^{\nu_2(2x)}$ and $g(x)=2x$ a 2-dimensional affine space on $\Bbb Z[\frac12]\setminus 0$?

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score 61 · Answer 15 · 2018-08-16 01:08:56

61

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Given $P_1,P_2\in \mathbb R^2$, integer $n>1$, and $f\in \mathbb R[X,Y]$, $f=g_1+g_2$, partial derivatives of order $<n$ of $g_i$ vanishing at $P_i$

Published on 16 Aug 2018 - 1:08

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