# Thread: Quick Facts on Orthogonal Matrices

1. ## Quick Facts on Orthogonal Matrices

Trying to verify some stuff for orthogonal matrices by making some factual statements. If I'm wrong, could I get some help or if someone could just say yes/no/right/wrong?

---> an orthogonal matrix doesn't guarantee that it is orthogonally diagonalizable. (I think... not sure)

---> The dimension of an eigenspace of a symmetric matrix equals the muiltiplicity of the corresponding eigenvalue.

2. Originally Posted by crystal-maiden
Trying to verify some stuff for orthogonal matrices by making some factual statements. If I'm wrong, could I get some help or if someone could just say yes/no/right/wrong?

---> an orthogonal matrix doesn't guarantee that it is orthogonally diagonalizable. (I think... not sure)

---> The dimension of an eigenspace of a symmetric matrix equals the muiltiplicity of the corresponding eigenvalue.
1) False. It is normal, so it is orthogonally diagble.

2) True. A symmetric matrix is diagonalizable, thus it is non-defective and thus geometric multiplicity = alg. multiplicity