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 93 · Answer 8 · 2026-04-12 17:18:50

93

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score 11.8k · Answer 9 · 2026-04-09 12:14:00

11.8k

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score 92 · Answer 10 · 2026-04-10 20:35:41

92

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score 98 · Answer 11 · 2026-04-15 13:17:45

98

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score 102 · Answer 12 · 2026-04-23 23:48:34

102

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score 492 · Answer 13 · 2026-03-25 15:45:28

492

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score 61 · Answer 14 · 2026-04-14 03:58:10

61

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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 64 · Answer 15 · 2026-04-15 17:28:42

64

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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 15 Apr 2026 - 17:28

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