Linear Algebra 15i: Dilation as a Linear Transformation

[vineetmukim]

Sir,
1) Is (x-1) the only Eigen-function of the given Dialation function which is polynomial of degree 1, because I am getting so?
2) Higher polynomial functions can be found by assuming a general form like Ax^2 + Bx + C and getting 2 simultaneous equations to give relation between A, B and C that satisfies the criteria. Isn't this algorithm robust enough?

[billchang]

I tried to picture a transformation of a zero vector into another zero vector, the problem 4 me is how to define a zero vector? is it simply zero?