(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Diagonalizing a 3x3 matrix

1. The problem statement, all variables and given/known data

I want to show that a real 3x3 matrix, A, whose square is the identity is diagonalizable by a real matrix P and that A has (real) eigenvalues of modulus 1.

2. Relevant equations

None.

3. The attempt at a solution

Since any matrix is diagonalizable over the complex numbers, I deduced that since there exists a complex matrix P such that PAP^{-1} = diag{x,y,z} (so x,y,z the eigenvalues of A), then diag{x^2,y^2,z^2} = (PAP^{-1})^2 = Id, hence the eigenvalues are square roots of 1 therefore must be real of modulus 1 as required.

I'm not totally sure my reasoning is sound. Even if it is, there is still the problem that P may be complex.

**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!

# Homework Help: Diagonalizing a 3x3 matrix

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