Thread: Linear Map and translation

Hi. Quick question:

6. Let T_u: V --> V be the translation by a vector u. For which vectors u is T_u a linear map?

Originally Posted by limddavid

Hi. Quick question:

6. Let T_u: V --> V be the translation by a vector u. For which vectors u is T_u a linear map?

A linear map has to map the zero vector to the zero vector, so...

Tonio

What must be true in order that a function be a linear map? In other words, what must you check?

(Here's a short cut- what must any linear map do to the 0 vector?)

Thanks for replying!

So I just check that T maps 0 to 0... And that is the only vector u that makes T a linear map?