$F$ is a function from $\mathbb{R}^2$ to $\mathbb{R}^2$. For every line $L$ in $\mathbb{R}^2$, $F(L)$ is a line, too. Also it maps origin to origin. Then, is $F$ a linear transform?
Asked
Active
Viewed 67 times
0
-
13blue1brown's video on the topic might enlighten you. – Arthur Mar 28 '24 at 16:14
-
think about a reflection in $\mathbb{R}^2$, is it linear? – Colver Mar 28 '24 at 16:16
-
1No. Consider a translation. – CyclotomicField Mar 28 '24 at 16:17
-
Do you consider translation a linear transform? – peterwhy Mar 28 '24 at 16:17
-
I changed the question. Sorry for confusion. – tneserp Mar 28 '24 at 16:26
-
2@Arthur: great piece of advice! Also, I think this is a very good question, but it should show some more effort to be upvoted. – Giuseppe Negro Mar 28 '24 at 16:48
-
1Various forms of this question were discussed a number of times on MSE, see for instance here and here, and in the linked questions. – Moishe Kohan Mar 29 '24 at 04:09
-
See also https://en.wikipedia.org/wiki/Collineation – GEdgar Mar 29 '24 at 06:55