Hey,(adsbygoogle = window.adsbygoogle || []).push({});

I know that if T(linear transformation in finite dim-vector space) is diagonalizable, then the matrix A that represent T is diagonalizable if there exist a matrix P=! 0 that is invertible and A=P^-1 * D * P for a diagonal matrix D.

I also know that raising A to a positive power will equal the right side with D raised to that same power. i.e. A^n = P^-1 * D^n * P

Does this imply that if T is diagonalizable so is T^2? what if T^2 is diagonalizable, then does that imply T is diagonalizable?

I think that it is an iff statement. Can anyone shine some light into this situation? maybe a counter example? is there a way to generalize the relationship between T and T^2?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Way to generalize the relationship between T and T^2?

**Physics Forums | Science Articles, Homework Help, Discussion**