How many Hecke operators span the Hecke algebra?

Linear algebra (Describe all linear operators T)?

• Describe all linear operators T∈Hom(R^2, R^2) such that T is diagonalizable and T^3-2T^2+T = 0.

• Answer:

  We can describe them via matrices. ------------- The characteristic polynomial must divide t^3 - 2t^2 + t = t(t - 1)^2. So, the eigenvalues are at most 0 and 1. Since T is diagonal, its matrix is similar to one of the following three: [1 0]..[0 0]......[0 0] [0 1],.[0 1], or.[0 0]. I hope this helps!