Answer to Question #198767 in Linear Algebra for Dhruv bartwal

Question

Let 0<θ<2π, θ ≠ π. Consider the linear transformation T: C^2→C^2 given by matrix

[ cosθ -sinθ] (w.r.t standard basis)

[ sinθ cosθ]. Find the vector v1, v2 such that T v1= (e^iθ)v1, T v2= (e^-iθ)v2. Is {v1,v2} a basis for C^2? Give reason for your answer