Linear Transformation and Diagonalization Problem

[Stapler2000]

Nevermind -- Polygons and Polywags.

 

[lanedance]

matrix in standard basis looks good, but i would check your characteristic polynomial

 

[lanedance]

i got x^2 - x + 6 = 0

 

[lanedance]

however as you mention it is correct that in the case T has complex eigenvalues it is not diagonalisable over the reals

 

[Stapler2000]

Agreed -- it is x^2-x+6.