Question

What is the relationship between the eigenvalues for `A` and for `c A` ?

Answer 1

See below.

Explanation:

The `A` characteristic polynomial is computed as

`det(A-lambda I_n)`

The `cA` characteristic polynomial is computed as

`det(cA-lambda I_n) = det(A-lambda/cI_n)`

then `A rArr p(lambda)` and `cA rArr p(lambda/c)`