1. May 9, 2005

Eus

Hi Ho! ^^v

I've some questions regarding linear transformation in my linear algebra course, guys!

Statement: A linear transformation is a special type of function.

My answer: Yes, it is a special type of function because it must satisfy the following properties from the definition of linear transformations which is
A transformation (or mapping) T is linear if:
1. T(c u + d v) = c T(u) + d T(v) for all u, v in the domain of T;
2. T(c u) = c T(u) for all u and all scalars c.

Am I right?

Statement: The superposition principle is a physical description of a linear transformation.
Note: In my book it is written, I rephrased it, the superposition principle is defined as the generalization of the definition of linear transformation (i.e. T(c1 v1 + ... + cp vp) = c1 T(v1) + ... + cp T(vp) for v1...vp in the domain of T and c1...cp are scalars)

My answer: Yes, it is because a physical event can be determined to be linear if the "input" conditions can be expressed as a linear combination of such "input" and the system's response is the same linear combination of the responses to the indiviual "input".

Am I right?

Thank you very much, guys!
Any help would be appreciated! ^^v

2. Jan 25, 2017

Joe Patroni

Yes, you are correct. Sorry you had to wait 12 years for an answer.